Random surface correlation functions
type: Item
instance of: scholarly article
title: Random surface correlation functions
zbMATH Open document ID: 0572.60019
DOI: 10.1007/BF01212530
published in: Communications in Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 81P20
zbMATH DE Number: 3913343
zbMATH Keywords: stochastic geometry
zbMATH Keywords: Truncated pair functions
zbMATH Keywords: random surface models
zbMATH Keywords: thermodynamic formalism
zbMATH Keywords: estimates of the entropy
author: D. B. Abraham
author: Jennifer T. Chayes
author: Lincoln Chayes
MaRDI profile type: Publication
cites work: On the validity of the inverse conjecture in classical density functional theory
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full work available at URL: https://doi.org/10.1007/bf01212530
OpenAlex ID: W2039361348
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description: scientific article; zbMATH DE number 3913343