Phase Separation and Coarsening in One-Dimensional Driven Diffusive Systems: Local Dynaimcs Leading to Long-Range Hamiltonians

Abstract

A driven system of three species of particle diffusing on a ring is studied in detail. The dynamics is local and conserves the three densities. A simple argument suggesting that the model should phase separate and break the translational symmetry is given. We show that for the special case where the three densities are equal the model obeys detailed balance and the steady-state distribution is governed by a Hamiltonian with asymmetric long-range interactions. This provides an explicit demonstration of a simple mechanism for breaking of ergodicity in one dimension. The steady state of finite-size systems is studied using a generalized matrix product ansatz. The coarsening process leading to phase separation is studied numerically and in a mean-field model. The system exhibits slow dynamics due to trapping in metastable states whose number is exponentially large in the system size. The typical domain size is shown to grow logarithmically in time. Generalizations to a larger number of species are discussed.

Revtex, 29 Pages, 7 figures, uses epsf.sty, submitted to Phys. Rev. E

References in corpus (6)

• Phase Separation in One-Dimensional Driven Diffusive Systems
• Spontaneous Breaking of Translational Invariance in One-Dimensional Stationary States on a Ring
• Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem
• N-species stochastic models with boundaries and quadratic algebras
• Smooth Phases, Roughening Transitions and Novel Exponents in One-dimensional Growth Models
• Exact Solution of Two-Species Ballistic Annihilation with General Pair-Reaction Probability

Cited by in corpus (71)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Macroscopic fluctuation theory
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Phase Coexistence in Driven One Dimensional Transport
• Thermodynamics and dynamics of systems with long-range interactions
• Criterion for phase separation in one-dimensional driven systems
• Exact solution of a cellular automaton for traffic
• Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Yang-Lee Theory for a Nonequilibrium Phase Transition
• Phase Transition in the ABC Model
• Novel phase-separation transition in one-dimensional driven models
• Strong Phase Separation in a Model of Sedimenting Lattices
• Long range correlations and phase transition in non-equilibrium diffusive systems
• Spectrum in multi-species asymmetric simple exclusion process on a ring
• Modelling one-dimensional driven diffusive systems by the Zero-Range Process
• Coarsening Dynamics of a Quasi One-dimensional Driven Lattice Gas
• Twenty five years after KLS: A celebration of non-equilibrium statistical mechanics
• Spurious phase in a model for traffic on a bridge
• Exact fluctuating hydrodynamics of active lattice gases -- Typical fluctuations
• Universality classes in two-component driven diffusive systems
• Phase transition in a non-conserving driven diffusive system
• Recursive structures in the multispecies TASEP
• Long-range correlations and ensemble inequivalence in a generalized ABC model
• Coarsening with non-trivial in-domain dynamics: correlations and interface fluctuations
• Dynamically generated hierarchies in games of competition
• Anomalous coarsening and glassy dynamics
• Phase fluctuations in the ABC model
• A reverse duality for the ASEP with open boundaries
• Steady state entropy production rate for scalar Langevin field theories
• Coarsening Dynamics in the Vicsek Model of Active Matter
• Aging processes in systems with anomalous slow dynamics
• Phase diagram and density large deviations of a nonconserving ABC model
• Current fluctuations at a phase transition
• Stochastic Dynamics of Discrete Curves and Multi-type Exclusion Processes
• Surface pattern formation and scaling described by conserved lattice gases
• Phase diagram of the ABC model with nonconserving processes
• Exactly solvable statistical model for two-way traffic
• Growth diversity in one dimensional fluctuating interfaces
• Ensemble inequivalence : Landau theory and the ABC model
• On the dynamical behavior of the ABC model
• On the absorbing-state phase transition in the one-dimensional triplet creation model
• Competition of coarsening and shredding of clusters in a driven diffusive lattice gas
• The grand canonical ABC model: a reflection asymmetric mean field Potts model
• Exact stationary state for a deterministic high speed traffic model with open boundaries
• Phase diagram of the ABC model with nonequal densities
• Coarsening of a Class of Driven Striped Structures
• On Matrix Product States for Periodic Boundary Conditions
• A mass transport model with a simple non-factorized steady-state distribution
• Evolution of the ABC model among the segregated configurations in the zero-temperature limit
• Phase separation transition of reconstituting k-mers in one dimension
• First order phase transition with a logarithmic singularity in a model with absorbing states
• Anomalous long-range correlations at a non-equilibrium phase transition
• Self-duality and shock dynamics in the $n$-component priority ASEP
• Vacancy-mediated domain growth in a driven lattice gas
• From conformal invariance to quasistationary states
• Relaxation processes in a system with logarithmic growth
• Microcanonical analysis of a nonequilibrium phase transition
• Phase diagram of a generalized ABC model on the interval
• From ABC to KPZ
• On energy solutions to stochastic Burgers equation
• Phase coexistence and spatial correlations in reconstituting k-mer models
• Slow dynamics in a driven two-lane particle system
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Unusual features of coarsening with detachment rates decreasing with cluster mass
• Drift of phase fluctuations in the ABC model
• The energy of the alphabet model
• Localization control of few-photon states in parity-symmetric photonic molecules under balanced pumping
• Inverse Ising inference, hyperuniformity and absorbing states in the Manna model