Phase transitions in systems possessing Shock solutions

Abstract

Recently it is shown that there are three families of stochastic one-dimensional non-equilibrium lattice models for which the single-shock measures form an invariant subspace of the states of these models. Here, both the stationary states and dynamics of single-shocks on a one-dimensional lattice are studied. This is done for both an infinite lattice and a finite lattice with boundaries. It is seen that these models possess both static and dynamical phase transitions. The static phase transition is the well known low-high density phase transition For the ASEP. The BCRW, and AKGP models also show the same phase transition. Double-shocks on a one-dimensional lattice are also investigated. It is shown that at the stationary state the contribution of double-shocks with higher width becomes small, and the main contribution comes from thin double-shocks.

21 pages, LaTeX2e, 1 figure, Phys. Rev. E to be appeared

References in corpus (18)

• Phase transitions in an exactly soluble one-dimensional exclusion process
• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• Partially Asymmetric Exclusion Process with Open Boundaries
• Localization of shocks in driven diffusive systems without particle number conservation
• Shock Profiles for the Asymmetric Simple Exclusion Process in One Dimension
• Reaction-Diffusion Processes of Hard-Core Particles
• Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems
• Exact shock measures and steady-state selection in a driven diffusive system with two conserved densities
• Multispecies reaction-diffusion systems
• Phase transition in an asymmetric generalization of the zero-temperature Glauber model
• Dynamical phase transition of a one-dimensional kinetic Ising model with boundaries
• Autonomous multispecies reaction-diffusion systems with more-than-two-site interactions
• Multiple Shocks in a Driven Diffusive System with Two Species of Particles
• Exact Shock Profile for the ASEP with Sublattice-Parallel Update
• Phase transitions in autonomous reaction-diffusion systems on a one-dimensional lattice with boundaries
• Phase transition in an asymmetric generalization of the zero-temperature q-state Potts model
• Numerical Study of Phase Transition in an Exclusion Model with Parallel Dynamics
• Exact Solution of a Reaction-Diffusion Model with Particle Number Conservation

Cited by in corpus (6)

• Multi shocks in Reaction-diffusion models
• Particle current fluctuations in a variant of asymmetric Glauber model
• Repelling Random Walkers in a Diffusion-Coalescence System
• Finite-dimensional representation of the quadratic algebra of a generalized coagulation-decoagulation model
• The Fokker-Planck equation, and stationary densities
• Multi-species reaction-diffusion models admitting shock solutions