A field-theoretical approach to the spin glass transition: models with long but finite interaction range

TL;DR

This paper investigates the behavior of spin glasses with finite interaction ranges using a field-theoretical approach, providing large-deviation estimates and analyzing the free energy of overlap interfaces near the critical temperature.

Contribution

It introduces a novel field-theoretical framework for spin glasses with finite interaction range and derives large-deviation functionals for overlap profiles.

Findings

Large-deviation functional describes overlap profiles for small interaction range

Upper bounds for overlap profile probabilities are established

Analysis of free energy cost of overlap interfaces near critical point

Abstract

We study spin glasses with Kac type interaction potential for small but finite inverse interaction range $\gamma$. Using the theoretical setup of coupled replicas, through the replica method we argue that the probability of overlap profiles can be expressed for small $\gamma$ through a large-deviation functional. This result is supported by rigorous arguments, showing that the large-deviation functional provides at least upper bounds for the probability. Finally we analyze the rate function, in the vicinity of the critical point $T_c=1$ of mean field theory, and we study the free energy cost of overlap interfaces, assuming the validity of a gradient expansion for the rate functional.