Phase Transition in Ferromagnetic Lattice Models on a Cayley Tree with Non-uniform External Magnetic Fields

ISBN: 978-981-08-8407-9

Authors: Nasir Ganikhodjaev

Abstract:

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 hx, x V, where V is the set of vertices of the Cayley tree. We show that both models on the Cayley tree with –J < inf {hx: x V} < sup{ hx: x V} < J, have a first-order phase transition. Keywords: Ising and Potts models; Phase transition; Cayley tree; non-uniform magnetic field.