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Random Current Representation for Transverse Field Ising Model

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Abstract

Random current representation (RCR) for transverse field Ising models (TFIM) has been introduced in [14]. This representation is a space-time version of the classical RCR exploited by Aizenman et. al. [1,3,4]. 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 the z-direction and address the issue of the sharpness of the phase transition.

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Authors and Affiliations

  1. Department of Statistics, UC Berkeley, Berkeley, CA, 94720, USA

    Nicholas Crawford

  2. Faculty of Industrial Engineering, Technion, Haifa, 3200, Israel

    Dmitry Ioffe

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  1. Nicholas Crawford
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  2. Dmitry Ioffe
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Correspondence to Dmitry Ioffe.

Additional information

Communicated by M. Aizenman

This research was supported by a grant from G.I.F., the German Israeli Foundation for Scientific Research and Development and by a grant from BSF, the United States—Israel Binational Science Foundation.

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Crawford, N., Ioffe, D. Random Current Representation for Transverse Field Ising Model. Commun. Math. Phys. 296, 447–474 (2010). https://doi.org/10.1007/s00220-010-1018-7

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  • DOI: https://doi.org/10.1007/s00220-010-1018-7

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