横场伊辛模型的随机电流表示
Random Current Representation for Transverse Field Ising Models
摘要：
最近，在\cite{ILN}中引入了横场伊辛模型的随机电流表示.这种表示是一个时空版本的经典随机电流表示利用Aizenman等。它是经典随机电流表示\cite{Ai82, ABF, AF}的时空版本。在本文中，我们制定和证明相应的时空版本的经典开关引理，并显示它们如何产生各种相关不等式。特别是，我们证明了截断两点函数在正磁场在$\sfz$方向的指数衰减和解决的问题的相变的尖锐性。
英文摘要：
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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