Asymmetrical Ising model on the Bethe lattice

The present paper deals with the statistical mechanics of an asymmetrical Ising mounted on the Bethe lattice. An asymmetrical Ising model is defined by assuming the spin variable of the usual Ising Hamiltonian to take up the eigenvalues 1, − λ, where λ is an asymmetry parameter. It is shown in this paper that an asymmetrical Ising model on the Bethe lattice without an external field does not favour any phase transition except for λ = 1. A phase transition is only observable when a λ-dependent external field-like term is added. The transition temperature Tc is derived in such a case and is found to increase with an increase of λ.