Dynamic Heterogeneity in the Glauber-Ising chain

TL;DR

This paper analyzes dynamic heterogeneity in the Glauber-Ising chain, revealing how multi-point correlations grow during coarsening, similar to glass formers, and clarifies the role of domain wall dynamics.

Contribution

It provides a detailed analysis of multi-point correlation functions in the Glauber-Ising chain, elucidating the nature of dynamic heterogeneity during coarsening.

Findings

Multi-point functions reveal growth of spatial correlations during coarsening.

Connected multi-point functions vanish in equilibrium, indicating no heterogeneity.

Scaling properties are interpreted via diffusion-annihilation of domain walls.

Abstract

In a recent paper [P. Mayer et al., Phys. Rev. Lett. 93, 115701 (2004)] it was shown, by means of experiments, theory and simulations, that coarsening systems display dynamic heterogeneity analogous to that of glass formers. Here, we present a detailed analysis of dynamic heterogeneities in the Glauber-Ising chain. We discuss how dynamic heterogeneity in Ising systems must be measured through connected multi-point correlation functions. We show that in the coarsening regime of the Ising chain these multi-point functions reveal the growth of spatial correlations in the dynamics, beyond what can be inferred from standard two-point correlations. They have non-trivial scaling properties, which we interpret in terms of the diffusion-annihilation dynamics of domain walls. In the equilibrium dynamics of the Ising chain, on the other hand, connected multi-point functions vanish exactly and dynamic heterogeneity is not observed. Our results highlight the similarities between coarsening systems and glass formers.