To describe spin glasses in terms of "pure states", it is necessary to average over the distribution of (possibly chaotic) states in a central region as one grows the system to infinite size. Newman and Stein have termed this distribution over states the "metastate". Recently Read has computed analytically the nature of correlations in the metastate in the mean field regime (d greater than 6) assuming replica symmetry breaking, finding results which agree with earlier work of Parisi et al.~for a presumably related quantity. The metastate may also be related to the non-equilibrium dynamics following a quench, in which correlations at short distance come to a steady state, one which may be influenced by the (out of equilibrium) fluctuations of spins at greater distance. Fisher and White term this the "maturation metastate". We [1] have computed the non-equilibrium dynamics of a one-dimensional model with long-range (LR) interactions corresponding to a short-range (SR) model in d = 8, i.e., in the mean field regime. Our results for correlations in this dynamic (maturation) metastate agree with the results of Read for the static metastate obtained using RSB. Hence, within the limits of the numerics, these results indicate that (i) RSB is valid in the mean field regime, and (ii) the dynamic and static metastates agree, at least in the mean field regime. The latter is particularly useful since static quantities are easier to calculate than dynamic ones. [1] Matthew Wittmann and A. P. Young, J. Stat. Mech. Theor. Exp. 013301 (2016), arXiv:1504.07709
40 years of Replica Symmetry Breaking
10-13 September 2019, Rome
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