Critical behavior of the two dimensional 2A->3A, 4A->0 binary system

TL;DR

This paper investigates the phase transitions of a two-dimensional reaction-diffusion model with site restrictions and diffusion, revealing complex reentrant behavior and different critical exponents depending on diffusion strength.

Contribution

It provides the first detailed analysis of the phase diagram and critical behavior of the 2A->3A, 4A->0 model in two dimensions, confirming reentrant phases and identifying distinct universality classes.

Findings

Reentrant phase diagram in diffusion-creation rate space.

Mean-field transition at zero branching rate with exponent 1/3.

Effective reaction dynamics dominate at weak diffusion with exponent 1/2.

Abstract

The phase transitions of the recently introduced 2A -> 3A, 4A -> 0 reaction-diffusion model (G.Odor, PRE 69 036112 (2004)) are explored in two dimensions. This model exhibits site occupation restriction and explicit diffusion of isolated particles. A reentrant phase diagram in the diffusion - creation rate space is confirmed in agreement with cluster mean-field and one-dimensional results. For strong diffusion a mean-field transition can be observed at zero branching rate characterized by $\alpha=1/3$ density decay exponent. In contrast with this for weak diffusion the effective 2A ->3A->4A->0 reaction becomes relevant and the mean-field transition of the 2A -> 3A, 2A -> 0 model characterized by $\alpha=1/2$ also appears for non-zero branching rates.