Exact correlation functions of Bethe lattice spin models in external fields

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.

19 pages

Cited by in corpus (16)

• Mean-field entanglement transitions in random tree tensor networks
• Exact phase diagrams for an Ising model on a two-layer Bethe lattice
• Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory
• Phase behaviour and structure of a superionic liquid in nonpolarized nanoconfinement
• Correlations in interacting systems with a network topology
• Equations of motion approach to the spin-1/2 Ising model on the Bethe lattice
• Residual entropy and waterlike anomalies in the repulsive one dimensional lattice gas
• Molecular correlations and solvation in simple fluids
• Statistical Mechanics Approach to the Holographic Renormalization Group: Bethe Lattice Ising Model and p-adic AdS/CFT
• Exact spin-spin correlation function for the zero-temperature random-field Ising model
• Scaling relations and finite-size scaling in gravitationally correlated lattice percolation models
• Semiflexible polymer on an anisotropic Bethe lattice
• The 6-vertex model of hydrogen-bonded crystals with bond defects
• Pressure exerted by a grafted polymer: Bethe lattice solution
• Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices
• Topological states and flat bands in exactly solvable decorated Cayley trees