Phase transitions of the binary production 2A->3A, 4A->0 model

TL;DR

This paper investigates phase transitions in a reaction-diffusion model with site restrictions and diffusion, revealing a reentrant transition line at finite branching rate and its universal behavior, challenging existing universality class classifications.

Contribution

It introduces a detailed analysis of phase transitions in the 2A->3A, 4A->0 model, including the discovery of a reentrant transition line and its universal properties, contrasting with previous mean-field results.

Findings

Reentrant phase transition line at finite branching rate for weak diffusion.

Universal behavior of the transition aligns with the PCPD model.

High diffusion rates lead to a mean-field transition only.

Abstract

Phase transitions of the 2A-> 3A, 4A->0 reaction-diffusion model is explored by dynamical, N-cluster approximations and by simulations.The model exhibits site occupation restriction and explicit diffusion of isolated particles. While the site mean-field approximation shows a single transition at zero branching rate introduced in PRE {\bf 67}, 016111 (2003), N>2 cluster approximations predict the appearance of another (reentrant) transition line for weak diffusion (D). This latter phase transition is continuous, occurs at finite branching rate and exhibits different scaling behavior. I show that the universal behavior of this transition is in agreement with that of the PCPD model both on the mean-field level and in one dimension. Therefore this model exhibiting annihilation by quadruplets does not fit in the recently suggested classification of universality classes of absorbing state transitions in one dimension (PRL {\bf 90}, 125701 (2003)). For high diffusion rates the effective 2A->3A->4A->0 reaction becomes irrelevant and the model exhibits a mean-field transition only. The two regions are separated by a non-trivial critical endpoint at D*.