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Surfaces and Peierls contours: 3-d wetting and 2-d Ising percolation

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Abstract

A natural model of a discrete random surface lying above a two-dimensional substrate is presented and analyzed. An identification of the “level curves” of the surface with the Peierls contours of Ising spin configurations leads to an exactly solvable free energy, with logarithmically divergent specific heat. The thermodynamic critical point is shown to be a wetting transition at which the surface height diverges. This is so even though the surface has no “downward fingers” and hence no “entropic repulsion” from the substrate.

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Authors and Affiliations

  1. Department of Theoretical Chemistry, 5, South Parks Rd., OX13UB, Oxford, England

    D. B. Abraham

  2. Department of Mathematics and Ariz. Center for Math. Sciences, University of Arizona, 85721, Tucson, AZ, USA

    C. M. Newman

Authors
  1. D. B. Abraham
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  2. C. M. Newman
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Communicated by A. Jaffe

Dedicated to Roland Dobrushin

Research supported in part by NSF Grant No. DMS-8514834 and AFOSR Contract No. F49620-86-C0130 under the U.R.I. program

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Abraham, D.B., Newman, C.M. Surfaces and Peierls contours: 3-d wetting and 2-d Ising percolation. Commun.Math. Phys. 125, 181–200 (1989). https://doi.org/10.1007/BF01217776

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  • DOI: https://doi.org/10.1007/BF01217776

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