A mathematical perspective on metastable wetting

Abstract

In this paper we investigate the dynamical behavior of an interface or polymer, in interaction with a distant attractive substrate. The interface is modeled by the graph of a nearest neighbor path with non-negative integer coordinates, and the equilibrium measure associates to each path \eta a probability proportional to \lambda^{H(\eta)} where \lambda is non-negative and H(\eta) is the number of contacts between \eta and the substrate at zero. The dynamics is the natural spin flip dynamics associated to this equilibrium measure. We let the distance to the substrate at both polymer ends be equal to aN, where 0 2/(1-2a) the mixing time is exponential in N and the system relaxes in an exponential manner which is typical of metastability.