What makes slow samples slow in the Sherrington-Kirkpatrick model

TL;DR

This study uses Monte Carlo simulations to analyze why certain disorder samples in the Sherrington-Kirkpatrick model exhibit slow relaxation, identifying correlations with specific observables and potential signs of temperature chaos.

Contribution

It provides the first detailed analysis linking relaxation times in the SK model to observable properties of disorder samples and explores the effects of system size and temperature.

Findings

Fast samples correlate with small largest eigenvalue of coupling matrix

Relaxation times are strongly correlated across different temperatures

Correlation with certain observables diminishes as system size increases

Abstract

Using results of a Monte Carlo simulation of the Sherrington-Kirkpatrick model, we try to characterize the slow disorder samples, namely we analyze visually the correlation between the relaxation time for a given disorder sample $J$ with several observables of the system for the same disorder sample. For temperatures below $T_c$ but not too low, fast samples (small relaxation times) are clearly correlated with a small value of the largest eigenvalue of the coupling matrix, a large value of the site averaged local field probability distribution at the origin, or a small value of the squared overlap $<q^2>$. Within our limited data, the correlation remains as the system size increases but becomes less clear as the temperature is decreased (the correlation with $<q^2>$ is more robust) . There is a strong correlation between the values of the relaxation time for two distinct values of the temperature, but this correlation decreases as the system size is increased. This may indicate the onset of temperature chaos.