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Random surface correlation functions

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Abstract

Truncated pair functions for free random surface models and Bernoulli ensembles are examined. In both cases, the pair function is shown to obey Ornstein-Zernike scaling whenever various correlation lengths of the system satisfy a nonperturbative criterion. Under the same conditions, the transverse displacement of surfaces contributing to the pair function is shown to be normally distributed. A new type of transition, which concerns the width of typical surfaces, is introduced and studied. Whenever the system is below the melting transition temperature of a related lower-dimensional model, the width of typical surfaces is shown to be finite. A thermodynamic formalism for free random surface models is developed. The formalism is used to obtain sharp estimates of the entropy of surfaces contributing to the pair function.

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Authors and Affiliations

  1. Department of Mathematics, University of Melbourne, 3052, Parkville, Vic., Australia

    D. B. Abraham

  2. Department of Physics, Harvard University, 02138, Cambridge, MA, USA

    J. T. Chayes & L. Chayes

Authors
  1. D. B. Abraham
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  2. J. T. Chayes
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  3. L. Chayes
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Additional information

Communicated by A. Jaffe

On leave from Department of Theoretical Chemistry, Oxford University, Oxford OX1 3TG, England

Work partially supported by the National Science Foundation under Grant No. PHY-8203669

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Abraham, D.B., Chayes, J.T. & Chayes, L. Random surface correlation functions. Commun.Math. Phys. 96, 439–471 (1984). https://doi.org/10.1007/BF01212530

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  • DOI: https://doi.org/10.1007/BF01212530

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