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

We develop a transfer matrix method to compute exactly the spin-spin correlation functions ^s0sn& of Bethe lattice spin models in the external magnetic field h and for any temperature T . We first compute ^s0sn& 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 spin1 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 j(T ,h) for the simple Ising model and BEG model, which show interesting scaling and divergent behavior as h→0 and T approaches the critical temperature Tc . Our method to compute exact spin-spin correlation functions may be applied to other Ising-type models on Bethe and Bethe-like lattices. @S1063-651X~98!13708-X#