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Effective field distribution and time-dependent order parameters of ising and heisenberg spin glasses

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Zeitschrift für Physik B Condensed Matter

Abstract

Spin Glasses are represented as assemblies of magnetic clusters interacting with random forces. It is shown that this model reduces to the Edwards-Anderson model by suitable scaling transformations of the variables, and that thereby several discrepancies between theory and experiment are eliminated. Then new computer simulation results are presented and analyzed. It is shown that the distribution of effective fields behaves asP(H eff)∝H 2eff (Heisenberg) orP(H eff)∝ const (Ising) for smallH eff, while it is a gaussian for largeH eff. In contrast to mean-field treatments of Klein, the width of this distribution has no drastic dependence on temperature. We then show that the Edwards-Anderson order parameter relaxes asq(t)∝τ A /t at high enough temperatures, while our recently introduced order parameterΨ(t)∝exp(−t/τ). Bothτ A ,τ and the susceptibilityχ Ψ seem to diverge at the freezing temperature, and the associated exponents are estimated. The smooth behavior of the specific heat is interpreted in terms of an exponentα < −1. While our description is qualitatively similar to the cluster percolation model of Smith, it is shown that the actualΨ-cluster distribution is not that of a percolation problem.

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  1. Fachrichtung 11.1 — Theoretische Physik, Universität des Saarlandes, D-6600, Saarbrücken, Federal Republic of Germany

    K. Binder

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Binder, K. Effective field distribution and time-dependent order parameters of ising and heisenberg spin glasses. Z Physik B 26, 339–349 (1977). https://doi.org/10.1007/BF01570744

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