Pair correlation function for spin glasses

TL;DR

This paper introduces a method to analyze spin glasses using a pair correlation function derived from Monte Carlo simulations, revealing how fluctuations scale with system size in different models.

Contribution

It presents a novel approach to extract pair correlation functions from overlap distributions and analyzes their size dependence in spin glass models.

Findings

In the Edwards-Anderson model, fluctuations are independent of system size.

In the Sherrington-Kirkpatrick model, fluctuations scale as 1/L and sqrt(L).

The measure w quantifies thermal fluctuations of magnetic patterns.

Abstract

We extract a pair correlation function (PCF) from probability distributions of the spin-overlap parameter q. The distributions come from Monte Carlo simulations. A measure, w, of the thermal fluctuations of magnetic patterns follows from the PCFs. We also obtain rms deviations (over different system samples) delta_p away from average probabilities for q. For the linear system-sizes $L$ we have studied, (i) w and delta_p are independent of L in the Edwards-Anderson model but scale as 1/L and sqrt{L}, respectively, in the Sherrington-Kirkpatrik model.