Phase Transitions in Ferromagnetic Ising Models with spatially dependent magnetic fields

Abstract

In this paper we study the nearest neighbor Ising model with ferromagnetic interactions in the presence of a space dependent magnetic field which vanishes as $|x{|}^{-\alpha }$, $\alpha >0$, as $|x|\to \infty$. We prove that in dimensions $d\ge 2$ for all $\beta$ large enough if $\alpha >1$ there is a phase transition while if $\alpha <1$ there is a unique DLR state.

to appear in Communications in Mathematical Physics

References in corpus (1)

• Phase Transition in the 1d Random Field ising model with long range interaction

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