Exact correlation functions of Bethe lattice spin models in external fields

TL;DR

This paper presents an exact transfer matrix method for calculating spin-spin correlation functions in Bethe lattice spin models under external fields, covering a broad class of models including Ising and BEG models.

Contribution

The authors develop a general transfer matrix approach to compute exact correlation functions for Bethe lattice spin models with external fields, applicable to various spin interactions.

Findings

Correlation length diverges near critical temperature.

Method applies to general spin-S Ising models.

Includes special cases like simple Ising and BEG models.

Abstract

We develop a transfer matrix method to compute exactly the spin-spin correlation functions of Bethe lattice spin models in the external magnetic field h and for any temperature T. We first compute the correlation function for the most general spin - S Ising model, which contains all possible single-ion and nearest-neighbor pair interactions. This general spin - S Ising model includes the spin-1/2 simple Ising model and the Blume-Emery-Griffiths (BEG) model as special cases. From the spin-spin correlation functions, we obtain functions of correlation length for the simple Ising model and BEG model, which show interesting scaling and divergent behavior as T approaches the critical temperature. Our method to compute exact spin-spin correlation functions may be applied to other Ising-type models on Bethe and Bethe-like lattices.