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

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.