Growth Kinetics in Systems with Local Symmetry

TL;DR

This paper studies the phase transition kinetics of 2D Ising gauge models, revealing a new universality class with unique growth laws and linking their asymptotic behavior to diffusion-reaction processes.

Contribution

It identifies the topological excitations governing kinetics in systems lacking a local order parameter and proposes a duality with diffusion-reaction processes.

Findings

Growth law: L(t) ~ (t/ln t)^{1/2}

Dynamical scaling observed during approach to equilibrium

Kinetics dual to 2D annihilating random walks

Abstract

The phase transition kinetics of Ising gauge models are investigated. Despite the absence of a local order parameter, relevant topological excitations that control the ordering kinetics can be identified. Dynamical scaling holds in the approach to equilibrium, and the growth of typical length scale is characteristic of a new universality class with $L(t)\sim \left(t/\ln t\right)^{1/2}$. We suggest that the asymptotic kinetics of the 2D Ising gauge model is dual to that of the 2D annihilating random walks, a process also known as the diffusion-reaction $A+A\to \hbox{inert}$.