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

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 $\nu =2.00$.

14 pages, 4 figures

Cited by in corpus (2)

• Disordered asymmetric simple exclusion process: mean-field treatment
• Real-space renormalisation group approach to driven diffusive systems