Critical behavior of random spin systems

TL;DR

This paper introduces a simple method to calculate critical exponents in dilute spin glasses without external fields, using an expansion of perturbed overlap averages related to the free energy and connectivity.

Contribution

It presents a novel, straightforward approach to determine critical exponents in dilute spin glasses through elementary calculations and overlap expansions.

Findings

Provides a strategy for calculating critical exponents with few calculations

Uses expansion of overlap averages related to free energy and connectivity

Assumes approximations about overlap monomials near critical point

Abstract

We provide a strategy to find in few elementary calculations the critical exponents of the overlaps for dilute spin glasses, in absence of external field. Such a strategy is based on the expansion of a suitably perturbed average of the overlaps, which is used in the formulation of the free energy as the difference between a cavity part and the derivative of the free energy itself, considered as a function of the connectivity of the model. We assume the validity of certain reasonable approximations, e.g. that higher powers of overlap monomials are of smaller magnitude near the critical point, of which we do not provide a rigorous proof.