Some non perturbative calculations on spin glasses

TL;DR

This paper investigates non-perturbative effects in spin glass models, focusing on metastable saddle points and their impact on free energy, using replica formalism and analyzing various models like REM, p-spin, and Potts.

Contribution

It introduces an ansatz for metastable saddle points and calculates their contribution to free energy in spin glass models, extending understanding beyond perturbative approaches.

Findings

Metastable saddle points significantly affect free energy calculations.

The ansatz provides a new way to estimate non-perturbative corrections.

Results apply to REM, p-spin, and p-state Potts models.

Abstract

Models of spin glasses are studied with a phase transition discontinuous in the Parisi order parameter. It is assumed that the leading order corrections to the thermodynamic limit of the high temperature free energy are due to the existence of a metastable saddle point in the replica formalism. An ansatz is made on the form of the metastable point and its contribution to the free energy is calculated. The Random Energy Model is considered along with the p-spin and the p-state Potts Models in their p < infinity expansion.