Exact spin–spin correlation functions of Bethe lattice Ising and BEG models in external fields

We develop a transfer matrix method to compute exactly the spin–spin correlation functions for Bethe lattice Ising model and Blume–Emery–Griffiths (BEG) model in the external magnetic field h and for any temperature T. The correlation length ξ(T,h) obtained from the spin–spin correlation function shows interesting scaling and divergent behavior as h→0 and T approaches the critical temperature Tc.