Random Current Representation for Transverse Field Ising Models
Abstract
Recently, a random current representation for transverse field Ising models has been introduced in ILN. This representation is a space-time version of the classical random current representation exploited by Aizenman et. al. %It is a space-time version of the classical random current representation Ai82, ABF, AF. In this paper we formulate and prove corresponding space-time versions of the classical switching lemma and show how they generate various correlation inequalities. In particular we prove exponential decay of truncated two-point functions at positive magnetic fields in -direction and address the issue of the sharpness of phase transition.
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