Free-Energy Barriers in the SK Model

TL;DR

This paper studies free-energy barriers in the SK spin-glass model using Monte Carlo simulations, confirming that the mean barrier height scales with system size as N^{1/3}, aligning with theoretical predictions.

Contribution

It demonstrates the finite-size scaling of free-energy barriers in the SK model and confirms the theoretical exponent using advanced simulation techniques.

Findings

Barrier height scales as N^{1/3}

Simulation results agree with theoretical predictions

Multi-overlap and parallel tempering methods are effective

Abstract

The Sherrington-Kirkpatrick spin-glass model is investigated by means of Monte Carlo simulations employing a combination of the multi-overlap algorithm with parallel tempering methods. We investigate the finite-size scaling behaviour of the free-energy barriers which are visible in the probability density of the Parisi overlap parameter. Assuming that the mean barrier height diverges with the number of spins N as N^alpha, our data show good agreement with the theoretical value alpha = 1/3.