Entropic repulsion for the high dimensional Gaussian lattice field between two walls

Hironobu Sakagawa

doi:10.1007/s10955-006-9049-3

Entropic repulsion for the high dimensional Gaussian lattice field between two walls

Hironobu Sakagawa

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

The main aim of this paper is to discuss the entropic repulsion of random interfaces between two hard walls. We consider the d (≥ 3)-dimensional Gaussian lattice field on ℝ^λ _N , λ _N = [-N, N] ^d ∩ ℤ^d and identify the repulsion of the field as N → ∞ under the condition that the field lies between two hard walls at the height level 0 and L in Λ _N where L is large enough but finite. We also study the same problem for two layered interfaces case.

Original language	English
Pages (from-to)	1255-1274
Number of pages	20
Journal	Journal of Statistical Physics
Volume	124
Issue number	5
DOIs	https://doi.org/10.1007/s10955-006-9049-3
Publication status	Published - 2006 Sep

Keywords

Entropic repulsion
Gaussian field
Gibbs measure
Hard wall
Random interface

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-006-9049-3

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title = "Entropic repulsion for the high dimensional Gaussian lattice field between two walls",

abstract = "The main aim of this paper is to discuss the entropic repulsion of random interfaces between two hard walls. We consider the d (≥ 3)-dimensional Gaussian lattice field on ℝλ N , λ N = [-N, N] d ∩ ℤd and identify the repulsion of the field as N → ∞ under the condition that the field lies between two hard walls at the height level 0 and L in Λ N where L is large enough but finite. We also study the same problem for two layered interfaces case.",

keywords = "Entropic repulsion, Gaussian field, Gibbs measure, Hard wall, Random interface",

author = "Hironobu Sakagawa",

note = "Funding Information: The author would like to thank Giambattista Giacomin for his helpful advises and Yvan Velenik for informing Griffith{\textquoteright}s inequality and interesting discussions. He also thanks anonymous referees for their useful remarks and careful reading of the paper. This work was partially supported by JSPS Postdoctoral Fellowships for Research Abroad. Copyright: Copyright 2006 Elsevier B.V., All rights reserved.",

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N2 - The main aim of this paper is to discuss the entropic repulsion of random interfaces between two hard walls. We consider the d (≥ 3)-dimensional Gaussian lattice field on ℝλ N , λ N = [-N, N] d ∩ ℤd and identify the repulsion of the field as N → ∞ under the condition that the field lies between two hard walls at the height level 0 and L in Λ N where L is large enough but finite. We also study the same problem for two layered interfaces case.

AB - The main aim of this paper is to discuss the entropic repulsion of random interfaces between two hard walls. We consider the d (≥ 3)-dimensional Gaussian lattice field on ℝλ N , λ N = [-N, N] d ∩ ℤd and identify the repulsion of the field as N → ∞ under the condition that the field lies between two hard walls at the height level 0 and L in Λ N where L is large enough but finite. We also study the same problem for two layered interfaces case.

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