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American Physical Society, Physical review E: Statistical, nonlinear, and soft matter physics, 1(74)

DOI: 10.1103/physreve.74.011107

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Phase transitions in systems possessing Shock solutions

Journal article published in 2005 by Maryam Arabsalmani ORCID, Amir Aghamohammadi
This paper is available in a repository.
This paper is available in a repository.

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Abstract

Recently it has been shown that there are three families of stochastic one-dimensional nonequilibrium 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 asymmetric simple exclusion process. The branching-coalescing random walk and asymmetric Kawasaki-Glauber process 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.