Evidence of non-mean-field-like low-temperature behavior in the Edwards-Anderson spin-glass model

TL;DR

This study uses large-scale Monte Carlo simulations to compare the low-temperature behaviors of the Edwards-Anderson and Sherrington-Kirkpatrick spin-glass models, revealing fundamental differences in their phase structures.

Contribution

It provides evidence that the Edwards-Anderson model exhibits a non-mean-field-like low-temperature phase with only a single pair of pure states, contrasting with the mean-field predictions.

Findings

Edwards-Anderson model shows a single pair of pure states at low temperatures.

Sherrington-Kirkpatrick model exhibits a different, more complex overlap distribution.

Results challenge the applicability of mean-field theory to finite-dimensional spin glasses.

Abstract

The three-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied via large-scale Monte Carlo simulations at low temperatures, deep within the spin-glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly different low-temperature behavior. The structure of the spin-glass overlap distribution for the Edwards-Anderson model suggests that its low-temperature phase has only a single pair of pure states.