Numerical results for the Edwards-Anderson spin-glass model at low temperature

TL;DR

This study provides numerical results for the Edwards-Anderson spin-glass model at low temperatures, revealing deviations from droplet and mean field theories through overlap distributions and surface fractal dimensions.

Contribution

The paper offers the first detailed numerical analysis of overlap distributions and excitation surface fractal dimensions in the EA model at low temperatures.

Findings

p(0)/T approaches 0.233(4) as T approaches 0

Fractal dimension of excitation surfaces d_s approaches 2.59(3) as T approaches 0

Results contrast with droplet and mean field theoretical predictions

Abstract

We have simulated Edwards-Anderson (EA) as well as Sherrington-Kirkpatrick systems of L^3 spins. After averaging over large sets of EA system samples of 3 =< L =< 10, we obtain accurate numbers for distributions p(q) of the overlap parameter q at very low temperature T. We find p(0)/T --> 0.233(4) as T --> 0. This is in contrast with the droplet scenario of spin glasses. We also study the number of mismatched links --between replica pairs-- that come with large scale excitations. Contributions from small scale excitations are discarded. We thus obtain for the fractal dimension of outer surfaces of q~0 excitations in the EA model d_s --> 2.59(3) as T tends to 0. This is in contrast with d_s --> 3 as T --> 0 that is predicted by mean field theory for the macroscopic limit.