Large Deviations in the Free-Energy of Mean-Field Spin-Glasses

TL;DR

This paper analytically calculates the probability of rare large deviations in the free energy of the Sherrington-Kirkpatrick spin-glass model, with results matching numerical data at zero temperature.

Contribution

It provides an exact analytical method for the large deviation distribution of free energy in mean-field spin glasses, extending understanding of their rare fluctuation behavior.

Findings

Analytical expression for large deviation probabilities

Quantitative agreement with numerical data at zero temperature

Method applicable to other mean-field disordered systems

Abstract

We compute analytically the probability distribution of large deviations in the spin-glass free energy for the Sherrington-Kirkpatrick mean field model, i.e. we compute the exponentially small probability of finding a system with intensive free energy smaller than the most likely one. This result is obtained by computing the average value of the partition function to the power $n$ as a function of $n$. At zero temperature this absolute prediction displays a remarkable quantitative agreement with the numerical data.