Cluster geometry and survival probability in systems driven by reaction-diffusion dynamics

TL;DR

This paper investigates a reaction-diffusion system with specific reactions, analyzing phase transitions, critical behavior, and cluster geometries, highlighting unique survival probabilities at the tricritical point.

Contribution

It introduces a reaction-diffusion model with multiple reactions, exploring phase transitions, critical behavior, and cluster structures, including the unique survival probability relationship at the tricritical point.

Findings

Different cluster structures at criticality for various phase behaviors

Existence of a linear relationship between survival probability and initial cluster size at the tricritical point

Critical behavior examined in 2+1 dimensions

Abstract

We consider a reaction-diffusion model incorporating the reactions A -> 0, A -> 2A and 2A -> 3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. As well as briefly examining this critical behavior in 2+1 dimensions, we pay particular attention to the cluster geometry. We observe the different cluster structures that form at criticality for the three different types of critical behavior and show that there exists a linear relationship for the probability of survival against initial cluster size at the tricritical point only.