Phase transitions in systems possessing Shock solutions

TL;DR

This paper investigates phase transitions in one-dimensional non-equilibrium lattice models with shock solutions, analyzing both static and dynamic transitions, and extends the study to double-shocks, revealing their contributions in stationary states.

Contribution

It provides a detailed analysis of static and dynamical phase transitions in models with shock measures, including the behavior of double-shocks and their contributions in stationary states.

Findings

Models exhibit static low-high density phase transitions similar to ASEP.

Double-shocks with higher width have negligible contributions in stationary states.

Both static and dynamical phase transitions are observed in the studied models.

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.