Exact correlation functions of Bethe lattice spin models in external fields

Details Exact correlation functions of Bethe lattice spin models in external fields Exact correlation functions of Bethe lattice spin models in external fields

1999-04-02

arxiv.org/abs/cond-mat/9904036v1

Phys. Rev. E 58, 1644 (1998)

Physics

Condensed Matter

Statistical Mechanics

19 pages

Scientific paper

10.1103/PhysRevE.58.1644

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.

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