A Position-Space Renormalization-Group Approach for Driven Diffusive Systems Applied to the Asymmetric Exclusion Model

TL;DR

This paper develops a position-space renormalization-group method for nonequilibrium driven diffusive systems and successfully applies it to the asymmetric exclusion model, accurately predicting critical points and exponents.

Contribution

It introduces a novel RG approach in the transition probability space for nonequilibrium systems and demonstrates its effectiveness on the asymmetric exclusion model.

Findings

Critical point at α_c=β_c=1/2 matches exact results

Critical exponent ν=2.71 approximates the exact value 2.00

Method provides a new tool for analyzing driven diffusive systems

Abstract

This paper introduces a position-space renormalization-group approach for nonequilibrium systems and applies the method to a driven stochastic one-dimensional gas with open boundaries. The dynamics are characterized by three parameters: the probability $\alpha$ that a particle will flow into the chain to the leftmost site, the probability $\beta$ that a particle will flow out from the rightmost site, and the probability $p$ that a particle will jump to the right if the site to the right is empty. The renormalization-group procedure is conducted within the space of these transition probabilities, which are relevant to the system's dynamics. The method yields a critical point at $\alpha_c=\beta_c=1/2$,in agreement with the exact values, and the critical exponent $\nu=2.71$, as compared with the exact value $\nu=2.00$.