Phase transition in ferromagnetic lattice models on a Cayley tree with non-uniform external magnetic fields - Ganikhodjaev, Nasir (Operations Research and Statistics 2011 & GST, 2011)

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In this article we study the phase transition phenomenon for the Ising and Potts models under the action of a non-uniform external magnetic field hx3 XE V, where V is the set of vertices of the Cayley tree. We show that both models on the Cayley tree with-J < inf {h,: xeV} < sup{ h,: x€V} < J, have a first-order phase tansition