Ising spin glass with arbitrary spin beyond the mean field theory

TL;DR

This paper extends the analysis of the Ising spin glass model to arbitrary spin values beyond the mean field approximation, focusing on critical temperature and susceptibility calculations using Bethe-Peierls approximation.

Contribution

It provides a novel application of Bethe-Peierls approximation to arbitrary spin Ising spin glasses, beyond the previously studied S=1/2 case.

Findings

Critical temperature as a function of system dimension and spin S.

Linear susceptibility dependence on system parameters.

Plots illustrating the dependence of critical properties.

Abstract

We consider the Ising spin glass for the arbitrary spin S with the short- ranged interaction using the Bethe- Peierls approximation previously formulated by Serva and Paladin for the same system but limited to S=1/2. Results obtained by us for arbitrary S are not a simple generalization of those for S=1/2. In this paper we mainly concentrate our studies on the calcutation of the citical temperature and the linear susceptibility in the paramagnetic phase as functions of the dimension of the system and spin number S. These dependences are illustrated by corresponding plots.