Journal of Statistical Physics

, Volume 160, Issue 6, pp 1545–1622 | Cite as

Wetting Transitions for a Random Line in Long-Range Potential

  • P. Collet
  • F. Dunlop
  • T. Huillet


We consider a restricted Solid-on-Solid interface in \(\mathbb {Z}_{+}\), subject to a potential \(V\left( n\right) \) behaving at infinity like \(-\text {w} /n^{2}\). Whenever there is a wetting transition as \(b_{0}\equiv \exp V\left( 0\right) \) is varied, we prove the following results for the density of returns \(m\left( b_{0}\right) \) to the origin: if \(\text {w}<-3/8\), then \( m\left( b_{0}\right) \) has a jump at \(b_{0}^{c}\); if \(-3/8<\text {w}<1/8\), then \(m\left( b_{0}\right) \sim \left( b_{0}^{c}-b_{0}\right) ^{\theta /\left( 1-\theta \right) }\) where \(\theta =1-\frac{\sqrt{1-8\text {w}}}{2}\); if \(\text {w}>1/8\), there is no wetting transition.


Random walks Solid-on-Solid model  Wetting transition 



The authors are grateful to the referees for useful remarks about the physical background.


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.CPHT, CNRS UMR-7644Ecole PolytechniquePalaiseau CedexFrance
  2. 2.LPTM, CNRS UMR-8089 and University of Cergy-PontoiseCergy-PontoiseFrance

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