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

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.

11pages, 19 figures. Added content and references. Accepted to Phys. Rev. E

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• Calculation of 1RSB transition temperature of spin glass models on regular random graphs under the replica symmetric ansatz
• Replica analysis of Franz-Parisi potential for sparse systems