Thermodynamic Construction of an One-Step Replica-Symmetry-Breaking Solution in Finite Connectivity Spin Glasses

TL;DR

This paper develops a one-step replica-symmetry-breaking solution for finite connectivity spin glasses, extending the replica symmetric solution and confirming its validity through Monte Carlo simulations.

Contribution

It introduces a novel one-step replica-symmetry-breaking solution for finite connectivity spin glasses using the replica method, extending previous solutions.

Findings

Solution aligns with cavity method results

Monte Carlo simulations validate the solution for K=2

Partial validation for K=3 near transition temperature

Abstract

An one-step replica-symmetry-breaking solution for finite connectivity spin-glass models with K body interaction is constructed at finite temperature using the replica method and thermodynamic constraints. In the absence of external fields, this construction provides a general extension of replica symmetric solution at finite replica number to one-step replica-symmetry-breaking solution. It is found that this result is formally equivalent to that of the one-step replica-symmetry-breaking cavity method. To confirm the validity of the obtained solution, Monte Carlo simulations are performed for K = 2 and 3. The thermodynamic quantities of the Monte Carlo results extrapolated to a large-size limit are consistent with those estimated by our solution for K = 2 at all simulated temperatures and for K = 3 except near the transition temperature.