A bound on the phase transition region for Ising models on closed cayley trees

We investigate further the general Ising model on closed Cayley trees and obtain an inner bound for the phase transition region parametrized by the intensity of pair interactions on the upper and lower trees. This bound implies the exact critical value for the symmetric Ising model that we have solved implicitly in our previous work. Another interesting special case, the antisymmetric Ising model in which the pair interactions on the upper and lower trees have opposite signs, is also treated.