Bethe lattice approximation of long-range interaction Ising models

An extension or modification of the usual Bethe lattice is used to approximate one-dimensional Ising models with long-range pair interactions of the form Σ ( J / m Θ )σ i σ i + m . In particular an expression is obtained which allows one to one to obtain the critical temperature, T c , as a function of Θ, in the approximation. Our results are compared to a number of other T c approximations.