Numerical Study of Phase Transition in an Exclusion Model with Parallel Dynamics

TL;DR

This paper introduces a numerical approach using Matrix Product Formalism to analyze phase transitions and shock formations in an exclusion process with parallel dynamics, revealing a complex phase diagram with multiple phases and second-order transitions.

Contribution

It presents a novel numerical method for studying phase behavior in exclusion models with parallel dynamics, highlighting the existence of multiple phases and shock phenomena.

Findings

Three distinct phases identified in the model

Second-order phase transitions separate the phases

Shock formation occurs at specific parameter values

Abstract

A numerical method based on Matrix Product Formalism is proposed to study the phase transitions and shock formation in the Asymmetric Simple Exclusion Process with open boundaries and parallel dynamics. By working in a canonical ensemble, where the total number of the particles is being fixed, we find that the model has a rather non-trivial phase diagram consisting of three different phases which are separated by second-order phase transition. Shocks may evolve in the system for special values of the reaction parameters.