Critical behavior of the massless free field at the depinning transition
Probability
2009-10-31 v1 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
We consider the d-dimensional massless free field localized by a delta-pinning of strength e. We study the asymptotics of the variance of the field, and of the decay-rate of its 2-point function, as e 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 e, for a broad class of d-dimensional massless models.
Keywords
Cite
@article{arxiv.math/0010291,
title = {Critical behavior of the massless free field at the depinning transition},
author = {Erwin Bolthausen and Yvan Velenik},
journal= {arXiv preprint arXiv:math/0010291},
year = {2009}
}