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An intermediate phase with slow decay of correlations in one dimensional 1/|x−y|2 percolation, Ising and Potts models

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We rigorously establish the existence of an intermediate ordered phase in one-dimensional 1/|x−y|2 percolation, Ising and Potts models. The Ising model truncated two-point function has a power law decay exponent θ which ranges from its low (and high) temperature value of two down to zero as the inverse temperature and nearest neighbor coupling vary. Similar results are obtained for percolation and Potts models.

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Authors and Affiliations

  1. Departments of Mathematics and Physics, Harvard University, 02138, Cambridge, MA, USA

    J. Z. Imbrie

  2. Department of Mathematics, University of Arizona, 85721, Tucson, AZ, USA

    C. M. Newman

Authors
  1. J. Z. Imbrie
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  2. C. M. Newman
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Additional information

Communicated by A. Jaffe

Alfred P. Sloan Research Fellow. Research supported in part by NSF Grants No. PHY-8706420 and PHY-8645122

Research supported in part by NSF Grant No. DMS-8514834 and AFOSR Contract F49620-86-C0130 at the Arizona Center for Math. Sciences

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Imbrie, J.Z., Newman, C.M. An intermediate phase with slow decay of correlations in one dimensional 1/|x−y|2 percolation, Ising and Potts models. Commun.Math. Phys. 118, 303–336 (1988). https://doi.org/10.1007/BF01218582

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  • DOI: https://doi.org/10.1007/BF01218582

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