First Order Phase Transition in a Reaction-Diffusion Model With Open Boundary: The Yang-Lee Theory Approach

TL;DR

This paper introduces a reaction-diffusion model with open boundaries that exhibits a first-order phase transition, analyzed through exact solutions, simulations, and Yang-Lee theory, demonstrating its applicability in non-equilibrium systems.

Contribution

The study provides an exactly solvable reaction-diffusion model with open boundaries showing a first-order phase transition, validated by analytical, numerical, and Yang-Lee theory methods.

Findings

Exact steady state weights calculated via matrix product method

Identification of a first-order phase transition between low and high-density phases

Validation of the phase diagram using Monte Carlo simulations and Yang-Lee theory

Abstract

A coagulation-decoagulation model is introduced on a chain of length L with open boundary. The model consists of one species of particles which diffuse, coagulate and decoagulate preferentially in the leftward direction. They are also injected and extracted from the left boundary with different rates. We will show that on a specific plane in the space of parameters, the steady state weights can be calculated exactly using a matrix product method. The model exhibits a first-order phase transition between a low-density and a high-density phase. The density profile of the particles in each phase is obtained both analytically and using the Monte Carlo Simulation. The two-point density-density correlation function in each phase has also been calculated. By applying the Yang-Lee theory we can predict the same phase diagram for the model. This model is further evidence for the applicability of the Yang-Lee theory in the non-equilibrium statistical mechanics context.