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Structure of gibbs states of one dimensional Coulomb systems

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Abstract

We present a method of computing the Coulomb forces on particles in an infinite configuration of charges in one dimension. The resolution of the apparent nonuniqueness in this problem leads to a structural proof of the translation symmetry breaking in jellium, at all temperatures, and to a related phenomenon of phase nonuniqueness in the two component system. The appropriate generalizations of the DLR and KMS conditions for these states are discussed.

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Authors and Affiliations

  1. Joseph Henry Laboratories, Physics Department, Princeton University, 08544, Princeton, N.J., USA

    Michael Aizenman

  2. Laboratoire de Physique Théorique, Ecole Polytechnique Fédérale de Lausanne, CH-1001, Lausanne, Switzerland

    Philippe A. Martin

Authors
  1. Michael Aizenman
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  2. Philippe A. Martin
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Additional information

Communicated by A. Jaffe

Supported in part by U.S. National Science Foundation, grant No. PHY-78 25390 A01

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Aizenman, M., Martin, P.A. Structure of gibbs states of one dimensional Coulomb systems. Commun.Math. Phys. 78, 99–116 (1980). https://doi.org/10.1007/BF01941972

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  • DOI: https://doi.org/10.1007/BF01941972

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