Phase Transition in Ferromagnetic Ising Models with Non-Uniform External Magnetic Fields

Abstract

In this article we study the phase transition phenomenon for the Ising model under the action of a non-uniform external magnetic field. We show that the Ising model on the hypercubic lattice with a summable magnetic field has a first-order phase transition and, for any positive (resp. negative) and bounded magnetic field, the model does not present the phase transition phenomenon whenever $\mathrm{liminf}{h}_i>0$, where $\mathbf{h}=(h_i{)}_{i\in {\mathbb{Z}}^d}$ is the external magnetic field.

11 pages. Published in Journal of Statistical Physics - 2010

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