Early time kinetics of systems with spatial symmetry breaking

TL;DR

This paper develops a generalized theory for the early evolution of systems with spatial symmetry breaking, identifying two distinct stages and validating predictions through numerical simulations of a long-range antiferromagnetic Ising model.

Contribution

It introduces a two-stage model for early symmetry-breaking dynamics, extending beyond linear theory, and confirms it with numerical simulations of long-range magnetic systems.

Findings

Two-stage evolution with symmetry-preserving and symmetry-breaking phases

Long-range interactions delay symmetry-breaking fluctuations

Fourier modes exhibit multiple exponential growth/decay behaviors

Abstract

In this paper we present a study of the early stages of unstable state evolution of systems with spatial symmetry changes. In contrast to the early time linear theory of unstable evolution described by Cahn, Hilliard, and Cook, we develop a generalized theory that predicts two distinct stages of the early evolution for symmetry breaking phase transitions. In the first stage the dynamics is dominated by symmetry preserving evolution. In the second stage, which shares some characteristics with the Cahn-Hilliard-Cook theory, noise driven fluctuations break the symmetry of the initial phase on a time scale which is large compared to the first stage for systems with long interaction ranges. To test the theory we present the results of numerical simulations of the initial evolution of a long-range antiferromagnetic Ising model quenched into an unstable region. We investigate two types of symmetry breaking transitions in this system: disorder-to-order and order-to-order transitions. For the order-to-order case, the Fourier modes evolve as a linear combination of exponentially growing or decaying terms with different time scales.