Random Current Representation for Transverse Field Ising Models

Details Random Current Representation for Transverse Field Ising Models Random Current Representation for Transverse Field Ising Models

2008-12-28

arxiv.org/abs/0812.4834v2

Physics

Mathematical Physics

22 pages

Scientific paper

Recently, a random current representation for transverse field Ising models has been introduced in \cite{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 \cite{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 $\sfz$-direction and address the issue of the sharpness of phase transition.

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