A bound on the phase transition region for Ising models on closed cayley trees
Zhongxing YeSchool of Electrical Engineering and Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USAToby BergerSchool of Electrical Engineering and Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA
1990en
ABI
Abstract
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.
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