Shock in a Branching-Coalescing Model with Reflecting Boundaries

TL;DR

This paper investigates phase transitions in a one-dimensional branching-coalescing model with reflecting boundaries, revealing two second-order transitions and shock structures in particle density profiles through numerical analysis of partition function zeros.

Contribution

It introduces a detailed analysis of phase transitions in a non-equilibrium model using Yang-Lee zeros, highlighting the role of particle density and shock formation.

Findings

Two second-order phase transitions identified

Transition points depend on particle density

Shock structures observed in density profiles

Abstract

A one-dimensional branching-coalescing model is considered on a chain of length L with reflecting boundaries. We study the phase transitions of this model in a canonical ensemble by using the Yang-Lee description of the non-equilibrium phase transitions. Numerical study of the canonical partition function zeros reveals two second-order phase transitions in the system. Both transition points are determined by the density of the particles on the chain. In some regions the density profile of the particles has a shock structure.