Influence of Disorder Strength on Phase Field Models of Interfacial Growth

We study the influence of disorder strength on the interface roughening process in a phase-field model with locally conserved dynamics. We consider two cases where the mobility coefficient multiplying the locally conserved current is either constant throughout the system (the two-sided model) or becomes zero in the phase into which the interface advances (one-sided model). In the limit of weak disorder, both models are completely equivalent and can reproduce the physical process of a fluid diffusively invading a porous media, where super-rough scaling of the interface fluctuations occurs. On the other hand, increasing disorder causes the scaling properties to change to intrinsic anomalous scaling. In the limit of strong disorder this behavior prevails for the one-sided model, whereas for the two-sided case, nucleation of domains in front of the invading front are observed.Comment: Accepted for publication in PR

Majority Rule Dynamics in Finite Dimensions

We investigate the long-time behavior of a majority rule opinion dynamics model in finite spatial dimensions. Each site of the system is endowed with a two-state spin variable that evolves by majority rule. In a single update event, a group of spins with a fixed (odd) size is specified and all members of the group adopt the local majority state. Repeated application of this update step leads to a coarsening mosaic of spin domains and ultimate consensus in a finite system. The approach to consensus is governed by two disparate time scales, with the longer time scale arising from realizations in which spins organize into coherent single-opinion bands. The consequences of this geometrical organization on the long-time kinetics are explored.Comment: 8 pages, 2-column revtex format, 11 figures. Version 2: minor changes in response to referee comments and typos corrected; final version for PR

Reentrant Behavior of the Spinodal Curve in a Nonequilibrium Ferromagnet

The metastable behavior of a kinetic Ising--like ferromagnetic model system in which a generic type of microscopic disorder induces nonequilibrium steady states is studied by computer simulation and a mean--field approach. We pay attention, in particular, to the spinodal curve or intrinsic coercive field that separates the metastable region from the unstable one. We find that, under strong nonequilibrium conditions, this exhibits reentrant behavior as a function of temperature. That is, metastability does not happen in this regime for both low and high temperatures, but instead emerges for intermediate temperature, as a consequence of the non-linear interplay between thermal and nonequilibrium fluctuations. We argue that this behavior, which is in contrast with equilibrium phenomenology and could occur in actual impure specimens, might be related to the presence of an effective multiplicative noise in the system.Comment: 7 pages, 4 figures; Final version to appear in Phys. Rev. E; Section V has been revise

Statistical physics of the Schelling model of segregation

We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics methods shed light on the rich phenomenology of this simple model, exhibiting static phase transitions typical of kinetic constrained models, nontrivial coarsening like in driven-particle systems and percolation-related phenomena.Comment: 4 pages, 3 figure

Stability of a Nonequilibrium Interface in a Driven Phase Segregating System

We investigate the dynamics of a nonequilibrium interface between coexisting phases in a system described by a Cahn-Hilliard equation with an additional driving term. By means of a matched asymptotic expansion we derive equations for the interface motion. A linear stability analysis of these equations results in a condition for the stability of a flat interface. We find that the stability properties of a flat interface depend on the structure of the driving term in the original equation.Comment: 14 pages Latex, 1 postscript-figur

Dynamics of mesoscopic precipitate lattices in phase separating alloys under external load

We investigate, via three-dimensional atomistic computer simulations, phase separation in an alloy under external load. A regular two-dimensional array of cylindrical precipitates, forming a mesoscopic precipitate lattice, evolves in the case of applied tensile stress by the movement of mesoscopic lattice defects. A striking similarity to ordinary crystals is found in the movement of "meso-dislocations", but new mechanisms are also observed. Point defects such as "meso-vacancies" or "meso-interstitials" are created or annihilated locally by merging and splitting of precipitates. When the system is subjected to compressive stress, we observe stacking faults in the mesoscopic one-dimensional array of plate-like precipitates.Comment: 4 pages, 4 figures, REVTE

Aging classification in glassy dynamics

We study the out of equilibrium dynamics of several models exhibiting aging. We attempt at identifying various types of aging systems using a phase space point of view: we introduce a trial classification, based on the overlap between two replicas of a system, which evolve together until a certain waiting time, and are then totally decoupled. We investigate in this way two types of systems, domain growth problems and spin glasses, and we show that they behave differently.Comment: 18 pages,9 Postscript figures,uses rotate.sty,epsf.st

Coarsening Kinetics of a Two Dimensional O(2) Ginzburg-Landau Model: Effect of Reversible Mode Coupling

We investigate, via numerical simulations, the phase ordering kinetics of a two- dimensional soft-spin O(2) Ginzburg-Landau model when a reversible mode cou- pling is included via the conserved conjugate momentum of the spin order parameter (the model E). Coarsening of the system, when quenched from a dis- ordered state to zero temperature, is observed to be enhanced by the existence of the mode coupling terms. The growth of the characteristic length scale L(t) exhibits an effective super-diffusive growth exponent that can be interpreted as a positive logarithmic-like correction to a diffusive growth, i.e., L(t) ~ (t ln t)^{1/2}. In order to understand this behavior, we introduced a simple phenomenological model of coarsening based on the annihilation dynamics of a vortex-antivortex pair, incorporating the effect of vortex inertia and logarithmically divergent mobility of the vortex. With a suitable choice of the parameters, numerical solutions of the simple model can fit the full simulation results very adequately. The effective growth exponent in the early time stage is larger due to the effect of the vortex inertia, which crosses over into late time stage characterized by positive logarithmic correction to a diffusive growth. We also investigated the non-equilibrium autocorrelation function from which the so called {\lambda} exponent can be extracted. We get {\lambda} = 1.99(2) which is distinctively larger than the value of {\lambda} = 1.17 for the purely dissipative model-A dynamics of non-conserved O(2) models.Comment: 19 pages, 8 figure

Coarsening in a Driven Ising Chain with Conserved Dynamics

We study the low-temperature coarsening of an Ising chain subject to spin-exchange dynamics and a small driving force. This dynamical system reduces to a domain diffusion process, in which entire domains undergo nearest-neighbor hopping, except for the shortest domains -- dimers -- which undergo long-range hopping. This system is characterized by two independent length scales: the average domain length L(t)~t^{1/2} and the average dimer hopping distance l(t)~ t^{1/4}. As a consequence of these two scales, the density C_k(t) of domains of length k does not obey scaling. This breakdown of scaling also leads to the density of short domains decaying as t^{-5/4}, instead of the t^{-3/2} decay that would arise from pure domain diffusion.Comment: 7 pages, 9 figures, revtex 2-column forma