Abstract:
We consider the d-dimensional massless free field localized by a δ-pinning of strength ɛ. We study the asymptotics of the variance of the field (when d= 2), and of the decay-rate of its 2-point function (when d≥ 2), as ɛ 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 ɛ, for a broad class of d-dimensional massless models.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 1 November 2000 / Accepted: 15 June 2001
Rights and permissions
About this article
Cite this article
Bolthausen, E., Velenik, Y. Critical Behavior of Massless Free Field at Depinning Transition. Commun. Math. Phys. 223, 161–203 (2001). https://doi.org/10.1007/s002200100542
Issue Date:
DOI: https://doi.org/10.1007/s002200100542