Study of the multi-species annihilating random walk transition at zero branching rate - cluster scaling behavior in a spin model

TL;DR

This paper investigates the critical behavior and cluster scaling in a one-dimensional spin model exhibiting a multi-species annihilating random walk transition at zero branching rate, revealing power laws and broken scaling laws.

Contribution

It provides a detailed analysis of the cluster behavior and scaling laws in a spin model with locally broken symmetry, focusing on the transition at zero branching rate.

Findings

Power law behaviors observed in both the phase transition point and active phase.

Hyperscaling law is fulfilled in the active phase.

Scaling laws connecting bulk and cluster exponents are broken due to the missing absorbing phase.

Abstract

Numerical and theoretical studies of a one-dimensional spin model with locally broken spin symmetry are presented. The multi-species annihilating random walk transition found at zero branching rate previously is investigated now concerning the cluster behaviour of the underlying spins. Generic power law behaviors are found, besides the phase transition point, also in the active phase with fulfillment of the hyperscaling law. On the other hand scaling laws connecting bulk- and cluster exponents are broken - a possibility in no contradiction with basic scaling assumptions because of the missing absorbing phase.