arXiv:cond-mat/9407091

Infinite Volume Relaxation in the Sherrington-Kirkpatrick Model

Ferraro, Giovanni

Published Jul 22, 1994• 4 citations

Abstract

In a recent work (Eissfeller and Opper, 1992) a numerical method has been proposed to simulate off-equilibrium zero-temperature parallel dynamics for the SK model without finite size effects. We study the extension of the method to non-zero temperature and sequential dynamics, and analyze more carefully the involved computational problems. We find evidence, in the glassy phase, for an algebraic relaxation of the energy density to its equilibrium value, at least at large enough temperatures, and for an algebraic relaxation of the magnetization to zero at non-zero temperatures, with an exponent directly proportional to the temperature.

DOI: 10.48550/arxiv.cond-mat/9407091

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arXiv:cond-mat/9407091

Infinite Volume Relaxation in the Sherrington-Kirkpatrick Model

Ferraro, Giovanni

Published Jul 22, 1994• 4 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/9407091

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N

and temperature

T

. Proper care is taken that the thermal fluctuations on the relaxation time estimates are totally negligible compared to the disorder induced fluctuations. The probability distribution of

\lnτ-\overline{\lnτ}

scales with the scaling variable

N^{1/3} (T_c-T)

strengthening the belief that

\overline{\lnτ}\propto N^{1/3}

in the whole spin glass phase.

An alternative method is applied to the nonequilibrium zero temperature dynamics of a Sherrington-Kirkpatrick model with nonsymmetric random exchange couplings

{\mathit{J}}_{\mathit{i}\mathit{j}}

\ensuremath{\ne}

{\mathit{J}}_{\mathit{j}\mathit{i}}

. Based on exact stochastic single spin equations for the infinite system, this mean-field Monte Carlo approach avoids the strong finite size effects of the usual simulations for this problem. Varying the average symmetry \ensuremath{\eta}=[

{\mathit{J}}_{\mathit{i}\mathit{j}}

{\mathit{J}}_{\mathit{j}\mathit{i}}

]/[

{\mathit{J}}_{\mathit{i}\mathit{j}}^{2}

], we find a clear transition from ergodic dynamics at \ensuremath{\eta}${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$=0.825 to a phase (\ensuremath{\eta}>${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$) where a finite fraction of the spins freezes. Only in the fully symmetric case \ensuremath{\eta}=1 is the entire system frozen.