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Exact correlation functions of Bethe lattice spin models in external fields

Chin-Kun Hu·N. Sh. Izmailian
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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.

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Chin-Kun Hu, N. Sh. Izmailian. 1999-04-02. Exact correlation functions of Bethe lattice spin models in external fields. https://doi.org/10.1103/physreve.58.1644

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