Erwin Bolthausen, Yvan Velenik
Critical Behavior of the massless free field at the depinning transition
(136K, Latex2e)
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.