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The random walk representation of classical spin systems and correlation inequalities

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Abstract

Ferromagnetic lattice spin systems can be expressed as gases of random walks interacting via a soft core repulsion. By using a mixed spinrandom walk representation we present a unified approach to many recently established correlation inequalities. As an application of these inequalities we obtain a simple proof of the mass gap for the λ(φ4)2 quantum field model. We also establish new upper bounds on critical temperatures.

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Author notes

  1. Jürg Fröhlich

    Present address: Theor. Physics, ETH, Zürich, Switzerland

Authors and Affiliations

  1. Departments of Mathematics and Physics, Indiana University, 47401, Bloomington, IN, USA

    David Brydges

  2. Institut des Hautes Etudes Scientifiques, 35 Route de Chartres, F-91440, Bures-sur-Yvette, France

    Jürg Fröhlich

  3. Courant Institute of Mathematical Sciences, 251 Mercer Street, 10012, New York, NY, USA

    Thomas Spencer

Authors
  1. David Brydges
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  2. Jürg Fröhlich
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  3. Thomas Spencer
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Additional information

Communicated by A. Jaffe

Partially supported by N.S.F. Grant No. 79-02490

On leave from the University of Virginia

Partially supported by N.S.F. Grant No. DMR 81-00417

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Brydges, D., Fröhlich, J. & Spencer, T. The random walk representation of classical spin systems and correlation inequalities. Commun.Math. Phys. 83, 123–150 (1982). https://doi.org/10.1007/BF01947075

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  • DOI: https://doi.org/10.1007/BF01947075

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