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

Jürg Fröhlich; Robert Israel; Elliot H. Lieb; Barry Simon

doi:10.1007/BF01940327

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

Jürg Fröhlich, Robert Israel, Elliot H. Lieb, Barry Simon

Mathematics

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291 Scopus citations

Abstract

We systematize the study of reflection positivity in statistical mechanical models, and thereby two techniques in the theory of phase transitions: the method of infrared 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.

Original language	English (US)
Pages (from-to)	1-34
Number of pages	34
Journal	Communications In Mathematical Physics
Volume	62
Issue number	1
DOIs	https://doi.org/10.1007/BF01940327
State	Published - Aug 1978

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01940327

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title = "Phase transitions and reflection positivity. I. General theory and long range lattice models",

abstract = "We systematize the study of reflection positivity in statistical mechanical models, and thereby two techniques in the theory of phase transitions: the method of infrared 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.",

author = "J{\"u}rg Fr{\"o}hlich and Robert Israel and Lieb, {Elliot H.} and Barry Simon",

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AB - We systematize the study of reflection positivity in statistical mechanical models, and thereby two techniques in the theory of phase transitions: the method of infrared 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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Phase transitions and reflection positivity. I. General theory and long range lattice models

Abstract

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