Publications

Emergent bath-mediated attraction and condensation arise when multiple particles are simultaneously driven through an equilibrated bath under geometric constraints. While such scenarios are observed in a variety of nonequilibrium phenomena with an abundance of experimental and numerical evidence, little quantitative understanding of how these interactions arise is currently available. Here we approach the problem by studying the behavior of two driven "tracer"particles, propagating through a bath in a 1D lattice with excluded-volume interactions. We apply the mean-field approximation to analytically explore the mechanism responsible for the tracers' emergent interactions and compute the resulting effective attractive potential. This mechanism is then numerically shown to extend to a realistic model of hard driven Brownian disks confined to a narrow 2D channel.

We study an interacting system of N classical particles on a line at thermal equilibrium. The particles are confined by a harmonic trap and repel each other via pairwise interaction potential that behaves as a power law proportional to Sigma i not equal j(N) vertical bar x(i) - x(j)vertical bar(-k) (with k > -2) of their mutual distance. This is a generalization of the well-known cases of the one-component plasma (k = -1), Dyson's log gas (k -> 0(+)), and the Calogero-Moser model (k = 2). Because of the competition between harmonic confinement and pairwise repulsion, the particles spread over a finite region of space for all k > -2. We compute exactly the average density profile for large N for all k > -2 and show that while it is independent of temperature for sufficiently low temperature, it has a rich and nontrivial dependence on k with distinct behavior for -2

We study the effect of a one-dimensional driving field on the interface between two coexisting phases in a two dimensional model. This is done by considering an Ising model on a cylinder with Glauber dynamics in all sites and additional biased Kawasaki dynamics in the central ring. Based on the exact solution of the two-dimensional Ising model, we are able to compute the phase diagram of the driven model within a special limit of fast drive and slow spin flips in the central ring. The model is found to exhibit two phases where the interface is pinned to the central ring: one in which it fluctuates symmetrically around the central ring and another where it fluctuates asymmetrically. In addition, we find a phase where the interface is centered in the bulk of the system, either below or above the central ring of the cylinder. In the latter case, the symmetry breaking is 'stronger' than that found in equilibrium when considering a repulsive potential on the central ring. This equilibrium model is analyzed here by using a restricted solid-on-solid model.

We study the effect of a single biased tracer particle in a bath of other particles performing the random average process (RAP) on an infinite line. We focus on the long time behavior of the mean and the fluctuations of the positions of the particles and also the correlations among them. In the long time t limit these quantities have well defined scaling forms and grow with time as yft. A differential equation for the scaling function associated with the correlation function is obtained and solved perturbatively around the solution for a symmetric tracer. Interestingly, when the tracer is totally asymmetric, further progress is enabled by the fact that the particles behind the tracer do not affect the motion of the particles in front of it, which leads in particular to an exact expression for the variance of the position of the tracer. Finally, the variance and correlations of the gaps between successive particles are also studied. Numerical simulations support our analytical results.

Mixed order phase transitions (MOT), which display discontinuous order parameter and diverging correlation length, appear in several seemingly unrelated settings ranging from equilibrium models with long-range interactions to models far from thermal equilibrium. In a recent paper [1], an exactly soluble spin model with long-range interactions that exhibits MOT was introduced and analyzed both by a grand canonical calculation and a renormalization group analysis. The model was shown to form a bridge between two classes of 1D models exhibiting MOT, namely between spin models with inverse distance square interactions and surface depinning models. In this paper, we elaborate on the calculations performed in [1]. We also analyze the model in the canonical ensemble, which yields a better insight into the mechanism of MOT. In addition, we generalize the model to include Potts and general Ising spins and also consider a broader class of interactions that decay with distance using a power law different from 2.

We show that the presence of a driven bond in an otherwise diffusive lattice gas with simple exclusion interaction results in long-range density-density correlation in its stationary state. In dimensions d>1 we show that in the thermodynamic limit this correlation decays as C(r,s)∼(r2+s2)-d at large distances r and s away from the drive with |r-s1. This is derived using an electrostatic analogy whereby C(r,s) is expressed as the potential due to a configuration of electrostatic charges distributed in 2d dimension. At bulk density ρ=1/2 we show that the potential is that of a localized quadrupolar charge. At other densities the same is correct in leading order in the strength of the drive and it is argued numerically to be valid at higher orders.

The denaturation transition of circular DNA is studied within a Poland-Scheraga-type approach, generalized to account for the fact that the total linking number (LK), which measures the number of windings of one strand around the other, is conserved. In the model the LK conservation is maintained by invoking both overtwisting and writhing (supercoiling) mechanisms. This generalizes previous studies, which considered each mechanism separately. The phase diagram of the model is analyzed as a function of the temperature and the elastic constant κ associated with the overtwisting energy for any given loop entropy exponent c. As in the case where the two mechanisms apply separately, the model exhibits no denaturation transition for c≤2. For c>2 and κ=0 we find that the model exhibits a first-order transition. The transition becomes of higher order for any κ>0. We also calculate the contribution of the two mechanisms separately in maintaining the conservation of the linking number and find that it is weakly dependent on the loop exponent c.

The condensation transition in a non-Markovian zero-range process is studied in one and higher dimensions. In the mean-field approximation, corresponding to infinite-range hopping, the model exhibits condensation with a stationary condensate, as in the Markovian case, but with a modified phase diagram. In the case of nearest-neighbor hopping, the condensate is found to drift by means of a slinky motion from one site to the next. The mechanism of the drift is explored numerically in detail. A modified model with nearest-neighbor hopping which allows exact calculation of the steady state is introduced. The steady state of this model is found to be a product measure, and the condensate is stationary.

The statistical mechanics of DNA denaturation under fixed linking number is qualitatively different from that of unconstrained DNA. Quantitatively different melting scenarios are reached from two alternative assumptions, namely, that the denatured loops are formed at the expense of (i) overtwist or (ii) supercoils. Recent work has shown that the supercoiling mechanism results in a picture similar to Bose-Einstein condensation where a macroscopic loop appears at T _c and grows steadily with temperature, while the nature of the denatured phase for the overtwisting case has not been studied. By extending an earlier result, we show here that a macroscopic loop appears in the overtwisting scenario as well. We calculate its size as a function of temperature and show that the fraction of the total sum of microscopic loops decreases above T _c, with a cusp at the critical point.

The effect of particle-nonconserving processes on the steady state of driven diffusive systems is studied within the context of a generalized ABC model. It is shown that in the limit of slow nonconserving processes, the large deviation function of the overall particle density can be computed by making use of the steady-state density profile of the conserving model. In this limit one can define a chemical potential and identify first order transitions via Maxwell's construction, similarly to what is done in equilibrium systems. This method may be applied to other driven models subjected to slow nonconserving dynamics.

We show that the presence of a localized drive in an otherwise diffusive system results in steady-state density and current profiles that decay algebraically to their global average value, away from the drive in two or higher dimensions. An analogy to an electrostatic problem is established, whereby the density profile induced by a driving bond maps onto the electrostatic potential due to an electric dipole located along the bond. The dipole strength is proportional to the drive, and is determined self-consistently by solving the electrostatic problem. The profile resulting from a localized configuration of more than one driving bond can be straightforwardly determined by the superposition principle of electrostatics. This picture is shown to hold even in the presence of exclusion interaction between particles.

The ABC model is a driven diffusive exclusion model, composed of three species of particles that hop on a ring with local asymmetric rates. In the weak asymmetry limit, where the asymmetry vanishes with the length of the system, the model exhibits a phase transition between a homogeneous state and a phase-separated state. We derive the exact solution for the density profiles of the three species in the hydrodynamic limit for arbitrary average densities. The solution yields the complete phase diagram of the model and allows the study of the nature of the first-order phase transition found for average densities that deviate significantly from the point of equal densities.

Systems with long-range interactions, while relaxing towards equilibrium, sometimes get trapped in long-lived non-Boltzmann quasistationary states (QSS) which have lifetimes that grow algebraically with the system size. Such states have been observed in models of globally coupled particles that move under Hamiltonian dynamics either on a unit circle or on a unit spherical surface. Here, we address the ubiquity of QSS in long-range systems by considering a different dynamical setting. Thus, we consider an anisotropic Heisenberg model consisting of classical Heisenberg spins with mean-field interactions and evolving under classical spin dynamics. Our analysis of the corresponding Vlasov equation for time evolution of the phase space distribution shows that in a certain energy interval, relaxation of a class of initial states occurs over a timescale which grows algebraically with the system size. We support these findings by extensive numerical simulations. This work further supports the generality of occurrence of QSS in long-range systems evolving under Hamiltonian dynamics.

We study entropy production and fluctuation relations in the restricted solid-on-solid growth model, which is a microscopic realization of the Kardar-Parisi-Zhang (KPZ) equation. Solving the one-dimensional model exactly on a particular line of the phase diagram we demonstrate that entropy production quantifies the distance from equilibrium. Moreover, as an example of a physically relevant current different from the entropy, we study the symmetry of the large deviation function associated with the interface height. In a special case of a system of length L = 4 we find that the probability distribution of the variation of height has a symmetric large deviation function, displaying a symmetry different from the Gallavotti-Cohen symmetry.

A generalization of the ABC model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) density-conserving or (ii) nonconserving dynamics. For equal average densities of the three species, both dynamical models are demonstrated to exhibit detailed balance with respect to a Hamiltonian with long-range interactions. The model is found to exhibit two distinct phase diagrams, corresponding to the canonical (density-conserving) and grand canonical (density nonconserving) ensembles, as expected in long-range interacting systems. The implications of this result to nonequilibrium steady states, such as those of the ABC model with unequal average densities, are briefly discussed.

We investigate the impact of supercoil period and nonzero supercoil formation energy on the thermal denaturation of a circular DNA. Our analysis is based on a recently proposed generalization of the Poland-Scheraga model that allows the DNA melting to be studied for plasmids with circular topology, where denaturation is accompanied by formation of supercoils. We find that the previously obtained first-order melting transition persists under the generalization discussed. The dependence of the size of the order-parameter jump at the transition point and the associated melting temperature are obtained analytically.

The impact of temporally correlated dynamics on nonequilibrium condensation is studied using a non-Markovian zero-range process (ZRP). We find that memory effects can modify the condensation scenario significantly: (i)For mean-field dynamics, the steady state corresponds to that of a Markovian ZRP, but with modified hopping rates which can affect condensation; (ii)for nearest-neighbor hopping dynamics in one dimension, the condensate is found to occupy two adjacent lattice sites and to drift with a finite velocity. The validity of these results in a more general context is discussed.

The pressure components of 'soft' disks in a two-dimensional narrow channel are analyzed in the dilute gas regime using the Mayer cluster expansion and molecular dynamics. Channels with either periodic or reflecting boundaries are considered. It is found that when the two-body potential, u(r), is singular at some distance r₀, the dependence of the pressure components on the channel width exhibits a singularity at one or more channel widths which are simply related to r₀. In channels with periodic boundary conditions and for potentials which are discontinuous at r₀, the transverse and longitudinal pressure components exhibit a 1/2 and a 3/2 singularity, respectively. Continuous potentials with a power-law singularity result in weaker singularities of the pressure components. For channels with reflecting boundary conditions the singularities are found to be weaker than those corresponding to periodic boundaries.

Nuclear pore complexes are constantly confronted by large fluxes of macromolecules and macromolecular complexes that need to get into and out of the nucleus. Such bidirectional traffic occurring in a narrow channel can easily lead to jamming. How then is passage between the nucleus and cytoplasm maintained under the varying conditions that arise during the lifetime of the cell? Here, we address this question using computer simulations in which the behaviour of the ensemble of transporting cargoes is analysed under different conditions. We suggest that traffic can exist in two distinct modes, depending on the concentration of cargoes and dissociation rates of the transport receptor-cargo complexes from the pores. In one mode, which prevails when dissociation is quick and cargo concentration is low, transport in either direction proceeds uninterrupted by transport in the other direction. The result is that the overall traffic direction fluctuates rapidly and unsystematically between import and export. Remarkably, when cargo concentrations are high and disassociation is slow, another mode takes over in which traffic proceeds in one direction for a certain extent of time, after which it flips direction for another period. The switch between this, more regulated, mode of transport and the other, quickly fluctuating state, does not require an active gating mechanism but rather occurs spontaneously through the dynamics of the transported particles themselves. The determining factor for the behaviour of traffic is found to be the exit rate from the pore channel, which is directly related to the activity of the Ran system that controls the loading and release of cargo in the appropriate cellular compartment.

Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r(d) at large distances r in d dimensions. As a result, these systems are non-additive and they display unusual thermodynamic and dynamical properties which are not present in systems with short range interactions. In particular, the various statistical mechanical ensembles are not equivalent and the microcanonical specific heat may be negative. Long range interactions may also result in breaking of ergodicity, making the maximal entropy state inaccessible from some regions of phase space. In addition, in many cases long range interactions result in slow relaxation processes, with time scales which diverge in the thermodynamic limit. Various models which have been found to exhibit these features are discussed.

We study theoretically layered spin systems where long-range dipolar interactions play a relevant role. By choosing a specific sample shape, we are able to reduce the complex Hamiltonian of the system to that of a much simpler coupled rotator model with short-range and mean-field interactions. This latter model has been studied in the past because of its interesting dynamical and statistical properties related to exotic features of long-range interactions. It is suggested that experiments could be conducted such that within a specific temperature range the presence of long-range interactions crucially affects the behavior of the system.

A class of non-local contact processes is introduced and studied using the mean field approximation and numerical simulations. In these processes particles are created at a rate which decays algebraically with the distance from the nearest particle. It is found that the transition into the absorbing state is continuous and is characterized by continuously varying critical exponents. This model differs from the previously studied non-local directed percolation model, where particles are created by unrestricted Levy flights. It is motivated by recent studies of non-equilibrium wetting indicating that such non-local processes play a role in the unbinding transition. Other non-local processes which have been suggested to exist within the context of wetting are considered as well.

We introduce a new XY mean-field spin system whose canonical and microcanonical thermodynamics can be solved exactly. Microcanonical entropy is obtained by a novel use of large deviation techniques. The model desplays ensemble inequivalence and the presence of negative specific heat and temperature jumps in the microcanonical ensemble.

We calculate the exact stationary distribution of the one-dimensional zero-range process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites and is uniquely characterized by a space-dependent fugacity which is a function of the boundary rates and the hopping asymmetry. For strong boundary drive the system has no stationary distribution. In systems which on a ring geometry allow for a condensation transition, a condensate develops at one or both boundary sites. On all other sites the particle distribution approaches a product measure with the finite critical density ρ _c . In systems which do not support condensation on a ring, strong boundary drive leads to a condensate at the boundary. However, in this case the local particle density in the interior exhibits a complex algebraic growth in time. We calculate the bulk and boundary growth exponents as a function of the system parameters.

The effective interaction between two probe particles in a one-dimensional driven system is studied. The analysis is carried out using an asymmetric simple exclusion process with nearest-neighbor interactions. It is found that the driven fluid mediates an effective long-range attraction between the two probes, with a force that decays at large distances x as -b/x, where b is a function of the interaction parameters. Depending on the amplitude b, the two probes may form one of three states: a) an unbound state, where the distance grows diffusively with time; b) a weakly bound state, in which the distance grows sub-diffusively; and c) a strongly bound state, where the average distance stays finite in the long-time limit. Similar results are found for the behavior of any finite number of probes.

The recently suggested correspondence between domain dynamics of traffic models and the asymmetric chipping model is reviewed. It is observed that in many cases traffic domains perform the two characteristic dynamical processes of the chipping model, namely chipping and diffusion. This correspondence indicates that jamming in traffic models in which all dynamical rates are non-deterministic takes place as a broad crossover phenomenon, rather than a sharp transition. Two traffic models are studied in detail and analyzed within this picture.

The dynamic and thermodynamical behavior of a gas of hard disks in a narrow channel was discussed. By using a virial expansion, it was found that the collision frequency and pressure curves exhibit a singularity at a channel width corresponding to twice the disk diameter. It was found that the maximum Lyapunov exponent also display a same behavior. The curves were dominated by solidlike configurations which are different from the bulk ones, at high density.

The study of Griffiths singularities occurring in unbinding of strongly disordered polymers was presented. The Lee-Yang zeros of partition sum were used to study a model with two randomly distributed binding energies. At a temperature, T_G = O(1), the model exhibited a Griffiths singularity corresponding to the melting of long homogeneous domains of the low binding energy.

The interstrand distance distribution between complementary base pairs of the two strands of a DNA molecule was studied near the melting transition. Scaling arguments, including self-avoiding interactions were presented for a generalized Poland-Scheraga-type model. Results for the distribution function just below the melting point were obtained. It was found that numerical simulations that take into account the self-avoiding interactions were in good agreement with the scaling approach.

An asymmetric exclusion process comprising positive particles, negative particles and vacancies is introduced. The model is defined on a ring and the dynamics does not conserve the number of particles. We solve the steady state exactly and show that it can exhibit a continuous phase transition in which the density of vacancies decreases to zero. The model has no absorbing state and furnishes an example of a one-dimensional phase transition in a homogeneous non-conserving system which does not belong to the absorbing state universality classes.

When DNA molecules are heated they undergo a denaturation transition by which the two strands of the molecule are separated and become unbound. Experimental studies strongly indicate that the denaturation transition is first order. The main theoretical approach to study this transition, introduced in the early 1960s, considers microscopic configurations of a DNA molecule as given by an alternating sequence of non-interacting bound segments and denaturated loops. Studies of this model usually neglect the repulsive, self-avoiding, interaction between different loops and segments and have invariably yielded continuous denaturation transitions. It is shown that the excluded volume interaction between denaturated loops and bound segments may be taken into account using recent results on the scaling properties of polymer networks of arbitrary topology. These interactions are found to drive the transition first order, compatible with experimental observations. The unzipping transition of DNA which takes place when the two strands are pulled apart by an external force acting on one end may also be considered within this approach, again yielding a first-order transition. Although the denaturation and unzipping transitions are thermodynamically first order, they do exhibit critical fluctuations in some of their properties. This appears, for example, in the algebraic decay of the loop size distribution at the thermal denaturation and in the divergence of the length of the end segment as the transition is approached in both thermal- and force-induced transitions.

A study of the ordering dynamics of the driven lattice-gas model was performed. The model was shown to evolve in two stages as depicted by the scaling arguments and extensive numerical simulations. The two stages were early stripe formation stage and a stripe coarsening stage. It was observed that multistriped state was thermodynamically stable.

The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher dimensions. In particular we study a system of three types of particles that diffuse under local conserving dynamics in two dimensions. Arguments and numerical studies are presented indicating that the coarsening process in any number of dimensions is logarithmically slow in time. A key feature of this behavior is that the interfaces separating the various growing domains are macroscopically smooth (well approximated by a Fermi function). This implies that the coarsening mechanism in one dimension is readily extendible to higher dimensions.

Keywords: ASYMMETRIC EXCLUSION MODEL; SPONTANEOUS SYMMETRY-BREAKING; DRIVEN DIFFUSIVE SYSTEMS; OPEN BOUNDARIES; CELLULAR AUTOMATA; TRANSLATIONAL INVARIANCE; STATIONARY STATES; PARALLEL DYNAMICS; STEADY-STATES; ISING-MODELS

A class of solid-on-solid growth models with short-range interactions and sequential updates is studied. The models exhibit both smooth and rough phases in dimension [Formula Presented]. Some of the features of the roughening transition which takes place in these models are related to contact processes or directed percolation type problems. The models are analyzed using a mean field approximation, scaling arguments, and numerical simulations. In the smooth phase the symmetry of the underlying dynamics is spontaneously broken. A family of order parameters which are not conserved by the dynamics is defined, as well as conjugate fields which couple to these order parameters. The corresponding critical behavior is studied, and novel exponents identified and measured. We also show how continuous symmetries can be broken in one dimension. A field theory appropriate for studying the roughening transition is introduced and discussed.

The phase diagram of a bulk cholesteric liquid crystal in an electric or magnetic field applied perpendicular to the pitch axis is studied. This is an example of a system which exhibits different types of phase transitions between various modulated and homogeneous states. Possible transitions are of three types: (1) first order, (2) continuous and described as a condensation of solitons with repulsive interaction, or (3) continuous but characterized by a small order parameter. The detailed behavior of the temperature-field phase diagram is found to be strongly dependent on the intrinsic chirality, where the existence of an undulating state is predicted at high chirality. The relevant temperature, electric field, and chirality ranges are experimentally attainable.

Modulated structures have been observed in nonchiral systems such as Langmuir monolayers and freely suspended smectic films, and a mechanism involving spontaneous chiral symmetry breaking has recently been suggested to account for the occurrence of these structures. We study a simple model corresponding to this mechanism in the mean-field approximation. We find that the model exhibits two uniaxially modulated phases (the director field is colinear or noncolinear) and a vortex-lattice phase, in addition to the two uniform ordered phases (one chiral and one nonchiral) and the disordered phase. The high-temperature transition from the uniform nonchiral phase to the noncolinear uniaxial phase is found to be of third order; it belongs to a peculiar, intermediate class of transitions that has previously been suggested to occur in chiral systems. The low-temperature transition from the noncolinear uniaxial phase to the uniform chiral phase is second order, but also peculiar, because the wave number vanishes linearly at the transition; the modulated phase just above the transition is best described as a spatially varying commensurate phase with walls.

A simple model of a driven diffusive system which exhibits spontaneous symmetry breaking in one dimension is introduced. The model has short range interactions and unbounded noise. It is characterized by an asymmetric exclusion process of two types of charges moving in opposite directions on an open chain. The model is studied by mean field and Monte Carlo methods. Exact solutions can be found in a restricted region of its parameter space. A simple physical picture for the symmetry breaking mechanism is presented.

The steady state distribution of polymer (or micelle) lengths under nonequilbrium conditions in which monomers are continuously extracted from a system is studied. The dynamical equations describing this process exhibit a one-parameter family of steady state distributions. A study of the dynamical equations suggests that they exhibit either a linear marginal or nonlinear marginal selection, depending on the control parameters of the model. The selection is explicitly demonstrated for a simplified linear version of the dynamical equations.

Evolving random cellular structures are observed to reach a universal scaling regime. A mean-field approach to finding fixed-point distributions in cell-side number is extended to distributions for the average area of cells with a given number of sides. This approach leads to simplified equations that can be analyzed analytically and numerically. The theorys results are compared to experimental results on dynamics and distributions in soap froths and good agreement is achieved.

The effect of a localized defect on the profile of a one-dimensional growing interface is considered. The (q, q') phase diagram of a restricted solid-on- solid growth model is studied within the mean field approximation, where q' and q are the intrinsic growth rates of the defect site and of all other sites, respectively. It is found that the model exhibits two types of phase transitions: One separating vanishing slope and non-vanishing slope inter­faces, and the other separating interfaces whose slope varies continuously with the defect parameter q' from those whose slope is independent of q'.

We review current attemps at understanding the scaling behavior of fully developed turbulence through studying simple, scalar, translationally invariant, deterministic coupled-map interface models. The universality classes of such model systems are discussed.

A model corresponding to the recently observed wrinkling transition in partially polymerized membranes is presented. In this model the quenched random internal disorder induced by the polymerization is coupled linearly to the local curvature of the membrane. It is argued that within the mean-field approximation the theory can be reduced to a Heisenberg spin-glass with random Dzyaloshinsky-Moriya interactions. It exhibits crumpled, flat, spin-glass (and mixed) phases with a phase transition from the flat to the glass (or mixed) phase. It is argued that these conclusions should also hold for non-self-avoiding membranes in D = 2.

Certain phase transitions in quasiperiodic systems are characterized by universal structures. In these cases the functional form of the order parameter corresponding to the modulated phase, P(r), is determined by the symmetry properties of the system and is independent of the details of the associated Landau-Ginzburg model. Here we consider a simple one-dimensional XY-like model corresponding to this type of phase transition. The universal modulated structure of this model is calculated numerically at various points along the critical line.

The stability of icosahedral, pentagonal, and other quasicrystalline phases to deformations which make them commensurate, and thus periodic, in one or more directions is analyzed. Although such deformations may be arbitrarily small, it is shown that quasicrystals are generically stable to them. Quasicrystals may therefore exist as thermodynamically stable phases. The possible symmetries which may arise in icosahedral structures when these deformations do take place are considered.

We present and analyze a new class of continuous phase transitions to incommensurate structures. This class is characterized by a small order parameter and diverging susceptibility, in common with instability-type transitions. However, the fundamental wave vector vanishes at the transition and the harmonic components of the order parameter are not small compared with the fundamental component, in common with nucleation-type transitions. These properties are shown to result from a gradient-cubic term in the free energy.

A neutron study of the tetragonal antiferromagnet FeGe2 has shown the existence of two continuous magnetic transitions at temperatures of 263 and 289 K. The upper temperature corresponds to a transition from paramagnetism to a basal-plane spiral structure propagating along the cell edges in that plane. At the lower temperature the spiral structure is transformed into the simple collinear structure previously reported in the literature. Typical critical behavior is observed at the upper temperature for individual satellite peaks. The spiral propagation vector decreases continuously to zero at the lower critical point, exhibiting power-law behavior with an exponent of 0.4070.005. Heat-capacity measurements reveal two -type anomalies with critical exponents in the expected range. The phase diagram has been analyzed using mean-field and renormalization-group considerations. A model based on zero basal-plane spin anisotropy yields a magnetic structure which agrees with the observed structure of the intermediate phase. The effect of an external field has also been treated theoretically.

The global phase diagram of a simple model exhibiting disorder-incommensurate (D-I) transition is analyzed using mean-field approximation. This phase diagram is expected to be qualitatively correct in d=3 dimensions. It is shown that depending on the parameters of this model, the D-I transition either (a) is associated with a small order parameter and may thus be described by a Landau-Ginzburg-Wilson model, or (b) has no small order parameter, and the transition takes place via condensation of solitons. The two segments of the transition line are connected by a line of first-order transitions. Applications to intercalate systems and to magnetic spirals are considered.

We present an exact solution of the long-time relaxational behavior of the magnetization in the Ising and XY chains in a quenched random field. The random field is assumed to be of infinite strength but present at only a fraction of the spin sites. We use Glauber dynamics for the Ising case, and a suitably generalized master equation for the XY case. In both models we find that for T=0, as time t, the magnetization decays as exp (-Ct13), where C is a constant. At finite temperatures the ultimate asymptotic behavior is purely exponential.

An exact derivation is given of the magnetic ground states for spin Ising modelswith pure four-spin interactions on the cubic lattices. The ordered states encompassferromagnetic, antiferromagnetic, and ferrimagnetic degenerate components, and theorder-parameter dimensionality is n=8, 4, and for the sc, the bcc, and the fcc lattices. The Landau-Ginzburg-Wilson Hamiltonians are derived for the sc and bcc lattices. Monte Carlo calculations demonstrate that the phase transition in all three lattices is of first order. The effects of a symmetry-breaking field are investigated for the bcc lattice. The phase diagram is calculated and shown to include lines of first-order and continuoustransitions as well as critical end points. The results are compared with mean-field and renormalization-group predictions.

It is shown by a calculation analogous to that carried out by Wallace and Zia for the pure Ising model that the lower critical dimension of the Ising model in a random field is 3 and not 2 as suggested by domain energy arguments. Further, the critical dimension for the roughening transition is shown to be 5 as compared to 3 for the pure Ising model.

Keywords: Physics, Applied

A model Hamiltonian for which a stable fixed point is not accessible is expected to yield a first-order transition. By applying a symmetry-breaking field, a continuous transition may be restored. The crossover from first-order to continuous transition induced by the most general quadratic symmetry-breaking field, g, for an n=2 cubic model, is studied using large-g expansion, mean-field, and renormalization-group calculations. It is shown that the (g,T) phase diagram is rather complex, exhibiting tricritical, fourth-order critical, and critical end points. This phase diagram may be realized in certain compounds corresponding to n=2 and n=3 cubic models such as Tb2(MoO4)3, BaTiO3, RbCaF3, and KMnF3.

Model Hamiltonians which possess no stable fixed point or which lie outside the domain of attraction of their stable fixed point, are known to yield first order transitions within the renormalization group approach. By applying a symmetry breaking field, g, a continuous transition may be restored. The crossover from first order to continuous transition induced by symmetry breaking fields is analyzed. Two Landau-Ginzburg-Wilson models are considered: (a) the n = 6-component model associated with type-I fcc antiferromagnets (such as UO₂), and (b) the n = 4-component model associated with type-II fcc antiferromagnets (such as TbP, TbAs, CeTe and TbSe). The symmetry breaking field corresponds to a magnetic field or a uniaxial stress. The phase diagrams are studied using large g expansions, means field calculations, and renormalization group techniques in d = 4-ε dimensions. It is found that the (g,T) phase diagrams are rather complex exhibiting fourth order critical points, tricritical points and critical end points.

The structural phase transition occurring in NbO₂ is analysed using renormalisation group techniques. It is suggested that the observed crossover in the order parameter critical exponent beta from beta approximately=0.19 to beta approximately=0.39 may reflect a crossover from Lifshitz to ordinary critical behaviour. The phenomenon is associated with the strongly anisotropic dispersion relation found in this compound.

Existing theories for commensurate-incommensurate transitions in one-dimensionally-modulated systems show that these transitions are continuous and are associated with domainwall formation. We consider the effect of domain-wall crossing in two-dimensionally modulated systems with hexagonal symmetry such as rare-gas layers adsorbed on graphite and the layered compound 2H-TaSe2. We show that if the commensurate-incommensurate transition is continuous, the hexagonal symmetry is broken in the incommensurate phase, while if the transition is first order the hexagonal symmetry can be maintained in the incommensurate phase. The experimental consequences of this prediction are discussed.

The global T-H→phase diagram of a model Hamiltonian associated with XY-like antiferromagnetic transitions in tetragonal crystals is studied. It is found that for sufficiently large fourth-order anisotropy (KJ0.0814), the model exhibits tricritical points at a finite nonzero magnetic field H→, in addition to the tetracritical point (T=TN, H→=0) predicted previously on the basis of a Landau-Ginzburg-Wilson analysis. The wing critical lines associated with one of the tricritical points are physically accessible in the T-H→ space. In a closely related model appropriate for uniaxial antiferromagnets, we find tricritical and fourth-order critical points at low temperatures.