Analysis of an Extended +-J Ising Spin Glass Model by Using a Gauge Symmetry

TL;DR

This paper uses gauge symmetry to analyze an extended +-J Ising spin glass model, deriving exact energy bounds and relations that are independent of lattice shape, and unifying various known solutions.

Contribution

It introduces a gauge symmetry approach to study an extended +-J Ising spin glass model, providing rigorous results and unifying existing solutions.

Findings

Exact internal energy derived

Rigorous upper bound of specific heat established

Unified solutions including Nishimori line and bond-diluted models

Abstract

We investigate an extended +-J Ising spin glass model by using a gauge symmetry. This model has +-J1 interactions and +-J2 interactions. We show that a gauge symmetry is usable to study this model. The exact internal energy, the rigorous upper bound of the specific heat and some rigorous relations for correlation functions and order parameters are shown by using the gauge symmetry. The results are rigorous, and do not depend on any lattice shape. A part of our results, e.g., the value of the exact internal energy should be useful for checking the computer programs for investigating this model. In addition, we find that the present solutions are general solutions which include the solutions on the so-called Nishimori line for the conventional +-J Ising spin glass model and the solutions for the bond-diluted +-J Ising spin glass model.