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Phase transitions and reflection positivity. I. General theory and long range lattice models

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Abstract

We systematize the study of reflection positivity in statistical mechanical models, and thereby two techniques in the theory of phase transitions: the method ofinfrared bounds and the chessboard method of estimating contour probabilities in Peierls arguments. We illustrate the ideas by applying them to models with long range interactions in one and two dimensions. Additional applications are discussed in a second paper.

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Author notes

  1. Jürg Fröhlich

    Present address: Institute des Hautes Études Scientifiques, 35, Route de Chartres, F-91440, Buressur-Yvette, France

Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada

    Robert Israel

  2. Departments of Mathematics and Physics, Princeton University, 08540, Princeton, NJ, USA

    Jürg Fröhlich, Elliot H. Lieb & Barry Simon

Authors
  1. Jürg Fröhlich
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  2. Robert Israel
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  3. Elliot H. Lieb
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  4. Barry Simon
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Additional information

Communicated by J. Glimm

Research partially supported by US National Science Foundation under Grant MPS-75-11864

Research partially supported by Canadian National Research Council under Grant A4015

Research partially supported by US National Science Foundation under Grant MCS-75-21684-A01

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Fröhlich, J., Israel, R., Lieb, E.H. et al. Phase transitions and reflection positivity. I. General theory and long range lattice models. Commun.Math. Phys. 62, 1–34 (1978). https://doi.org/10.1007/BF01940327

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  • DOI: https://doi.org/10.1007/BF01940327

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