Dynamic Heterogeneity in the GlauberIsing chain.pdf

5 0 0 2 Dynamic Heterogeneity in the Glauber-Ising chain b e F †,‡ ‡ §,|| Peter Mayer , Peter Sollich , Ludovic Berthier and Juan P. 0 Garrahan¶ 1 †Department of Chemistry, Columbia University, 3000 Broadway, New York, NY ] h 10027, US c ‡Department of Mathematics, King’s College, Strand, London, WC2R 2LS, UK e m §Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP, UK - ||Laboratoire des Collo¨ıdes, Verres et Nanomat´eriaux, Universit´e Montpellier II and t UMR 5587 CNRS, 34095 Montpellier Cedex 5, France a t ¶School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 s t. 2RD, UK a m- Abstract. In a recent paper [P. Mayer et al., Phys. Rev. Lett. 93, 115701 (2004)] it d was shown, by means of experiments, theory and simulations, that coarsening systems n display dynamic heterogeneity analogous to that of glass formers. Here, we present a o c detailed analysis of dynamic heterogeneities in the Glauber-Ising chain. We discuss how [ dynamic heterogeneity in Ising systems must be measured through connected multi- 1 point correlation functions. We show that in the coarsening regime of the Ising chain v these multi-point functions reveal the growth of spatial correlations in the dynamics, 1 beyond what can be inferred from standard two-point correlations. They have non- 7 2 trivial scaling properties, which we interpret in terms of the diffusion-annihilation 2