Distribution of time scales in the Sherrington-Kirkpatrick model

TL;DR

This paper uses Monte Carlo simulations to analyze the distribution of equilibrium relaxation times in the Sherrington-Kirkpatrick model, revealing scaling behavior related to system size and temperature.

Contribution

It provides numerical evidence for the scaling of relaxation time distributions in the spin glass phase of the SK model, emphasizing disorder-induced fluctuations.

Findings

Distribution of ln(τ) scales with N^{1/3}(T_c - T)

Thermal fluctuations are negligible compared to disorder fluctuations

Average ln(τ) scales as N^{1/3}

Abstract

Numerical data on the probability distribution of the equilibrium relaxation time of the Sherrington-Kirkpatrick model are obtained by means of dynamical Monte Carlo simulation, for several values of the system size $N$ 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 $\ln\tau-\overline{\ln\tau}$ scales with the scaling variable $N^{1/3} (T_c-T)$ strengthening the belief that $\overline{\ln\tau}\propto N^{1/3}$ in the whole spin glass phase.