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Critical behavior of the massless free field at the depinning transition


Bolthausen, E; Velenik, Y (2001). Critical behavior of the massless free field at the depinning transition. Communications in Mathematical Physics, 223(1):161-203.

Abstract

We consider the d-dimensional massless free field localized by a δ-pinning of strength ɛ. We study the asymptotics of the variance of the field (when d= 2), and of the decay-rate of its 2-point function (when d≥ 2), as ɛ goes to zero, for general Gaussian interactions. Physically speaking, we thus rigorously obtain the critical behavior of the transverse and longitudinal correlation lengths of the corresponding d+ 1-dimensional effective interface model in a non-mean-field regime. We also describe the set of pinned sites at small ɛ, for a broad class of d-dimensional massless models.

Abstract

We consider the d-dimensional massless free field localized by a δ-pinning of strength ɛ. We study the asymptotics of the variance of the field (when d= 2), and of the decay-rate of its 2-point function (when d≥ 2), as ɛ goes to zero, for general Gaussian interactions. Physically speaking, we thus rigorously obtain the critical behavior of the transverse and longitudinal correlation lengths of the corresponding d+ 1-dimensional effective interface model in a non-mean-field regime. We also describe the set of pinned sites at small ɛ, for a broad class of d-dimensional massless models.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:asymptotics of the variance; interface; wetting transition
Language:English
Date:2001
Deposited On:27 Apr 2010 11:36
Last Modified:19 Feb 2018 22:02
Publisher:Springer
ISSN:0010-3616
Additional Information:The original publication is available at www.springerlink.com
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s002200100542
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1860764
http://www.zentralblatt-math.org/zmath/en/search/?q=an:0992.82011

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