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Physical review. B, Condensed matter

Remanent magnetization decay at the spin-glass critical point: A new dynamic critical exponent for nonequilibrium autocorrelations

David A. Huse

Published Jul 1, 1989• 252 citations
Publisher

Abstract

A quench of a d-dimensional spin system from a random initial configuration, {${\mathrm{S}}_{i}$(0)}, to a critical point is considered. The decay with time t of the autocorrelation with the initial condition is ${q}_{0}$(t)==〈${\mathrm{S}}_{i}$(0)\ensuremath{\cdot}${\mathrm{S}}_{i}$(t)〉\ensuremath{\sim}${t}_{\mathit{c}}^{\ensuremath{-}\ensuremath{\lambda}}$/z, where z is the usual dynamic critical exponent. Naively, ${\ensuremath{\lambda}}_{c}$=d, but I find ${\ensuremath{\lambda}}_{c}$simulations of pure Ising models in d=2, 3 and the \ifmmode\pm\else\textpm\fi{}J Ising spin glass in d=3. This suggests that ${\ensuremath{\lambda}}_{c}$ is a new critical exponent for nonequilibrium dynamics. For a spin glass the decay of ${q}_{0}$(t) is the same as that of the remanent magnetization; the exponent ${\ensuremath{\lambda}}_{c}$/z observed in the spin-glass simulation is in good agreement with a recent experimental measurement by Granberg et al.

DOI
10.1103/physrevb.40.304

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I present an analysis of the dynamic behavior of short-range Ising spin glasses observed in stochastic simulations. The time dependence of the order parameter q(t)=〈Sx{S}_{x}Sx​(0)Sx{S}_{x}Sx​(t)〉\ifmmode\bar\else\textasciimacron\fi{}---which is the same as that of the structure factor---and the time dependence of the related dynamic correlation functions have been recorded with good statistics and very long observation times. The spin-glass model with a symmetric distribution of discrete nearest-neighbor \ifmmode\pm\else\textpm\fi{}J interactions on a simple-cubic lattice was used. Simulations were performed with a special fast computer, allowing for the first-time investigation of the equilibrium dynamics for a wide range of temperatures (0.7\ensuremath{\le}kT/J\ensuremath{\le}5.0) and lattice sizes (83{8}^{3}83, 163{16}^{3}163, 323{32}^{3}323, and 643{64}^{3}643). I have found that the empirical formula q(t)=${\mathrm{ct}}^{\mathrm{\ensuremath{-}}x}$exp(-\ensuremath{\omega}${t}^{\ensuremath{\beta}}$) with temperature-dependent exponents x(T) and \ensuremath{\beta}(T) describes the decay very well at all temperatures above the spin-glass transition. In the spin-glass phase, only the algebraic decay q(t)=${\mathrm{ct}}^{\mathrm{\ensuremath{-}}x}$ could be observed, with different temperature dependences of the exponent x(T). The dynamic scaling hypothesis and finite-size scaling explain well the observed temperature and size dependence of the data, and the functional form of the correlation functions is com- patible with the scaling form if corrections to scaling are taken into account. The scaling behavior and the dynamic and static critical exponents found in my simulations are in reasonable agreement with recent experiments performed on insulating spin glasses, showing that despite its simplicity the discrete model of spin glasses analyzed in this work displays behavior similar to that seen in nature.