Critical behavior of the massless free field at the depinning transition

Details Critical behavior of the massless free field at the depinning transition Critical behavior of the massless free field at the depinning transition

2000-10-30

arxiv.org/abs/math/0010291v1

Commun.Math.Phys. 223 (2001) 161-203

Mathematics

Probability

Scientific paper

10.1007/s002200100542

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.

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