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Abstract

Critical Behavior of the Massless Free Field at the Depinning Transition E. Bolthausen and Y. Velenik Commun. Math. Phys. 223, 161-203 (2001). We consider the d-dimensional massless free field localized by a $\delta$-pinning of strength epsilon. We study the asymptotics of the variance of the field (when $d=1$ or $2$), and of the decay-rate of its 2-point function (for all $d$), as epsilon 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 epsilon, for a broad class of $d$-dimensional massless models. Key words: Gradient models, massless free field, effective interface model, pinning, critical behaviour, critical exponents, correlation lengths. Files: PDF file, Published version, bibtex