Existence of the free energy for heavy-tailed spin glasses

TL;DR

This paper proves the existence and self-averaging property of the free energy in a mean-field spin glass model with heavy-tailed couplings, specifically with infinite variance but finite mean.

Contribution

It establishes the thermodynamic limit and self-averaging of free energy for spin glasses with power law distributed couplings with infinite variance.

Findings

Thermodynamic limit of free energy exists.

Free energy is self-averaging.

Model involves heavy-tailed couplings with infinite variance.

Abstract

We study the free energy of a mean-field spin glass whose coupling distribution has power law tails. Under the assumption that the couplings have infinite variance and finite mean, we show that the thermodynamic limit of the quenched free energy exists, and that the free energy is self-averaging.