We provide a new approach to study phase transition for Ising models on closed Cayley trees. It is shown that there may exist more than one limiting measure for an Ising model on an infinite Cayley tree in both ferromagnetic and antiferromagnetic cases. The exact critical values of the...

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...