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

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

2010-01-20

arxiv.org/abs/1001.3443v2

Journal of Statistical Physics - 2010

Physics

Mathematical Physics

11 pages

Scientific paper

10.1007/s10955-010-9961-4

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 $\liminf h_i> 0$, where ${\bf h} = (h_i)_{i \in \Z^d}$ is the external magnetic field.

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