The Derivation of the Exact Internal Energies for Spin Glass Models by Applying the Gauge Theory to the Fortuin-Kasteleyn Representation

TL;DR

This paper derives exact internal energies and bounds for specific heats in spin glass models using gauge theory and the Fortuin-Kasteleyn representation, focusing on Nishimori lines.

Contribution

It introduces a novel method applying gauge theory to the Fortuin-Kasteleyn representation for deriving physical quantities in spin glasses.

Findings

Exact internal energies derived for spin glass models.

Rigorous upper bounds of specific heats established.

Results consistent with previous solutions.

Abstract

We derive the exact internal energies and the rigorous upper bounds of specific heats for several spin glass models by applying the gauge theory to the Fortuin-Kasteleyn representation which is a representation based on a percolation picture for spin-spin correlation. The results are derived on the Nishimori lines which are special lines on the phase diagrams. As the spin glass models, the +-J Ising model and a Potts gauge glass model are studied. The present solutions agree with the previous solutions. The derivation of the solutions by the present method must be useful for understanding the relationship between the percolation picture for spin-spin correlation and the physical quantities on the Nishimori line.