Dynamic Heterogeneity in the Glauber-Ising chain

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.

18 pages, 4 figures

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Cited by in corpus (10)

• Modified fluctuation-dissipation theorem near non-equilibrium states and applications to the Glauber-Ising chain
• Scaling and super-universality in the coarsening dynamics of the 3d random field Ising model
• Fluctuations in the coarsening dynamics of the O(N) model: are they similar to those in glassy systems?
• Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
• Non-linear susceptibilities of spherical models
• Fluctuations and effective temperatures in coarsening
• Finite-size scaling in the ageing dynamics of the $1D$ Glauber-Ising model
• Dynamic heterogeneities in critical coarsening: Exact results for correlation and response fluctuations in finite-sized spherical models (Version 2)
• Fluctuations of two-time quantities and non-linear response functions
• Exact solution of the Glauber-Ising model on the finite-length semi-open chain