Finite-size effects at wetting transitions.

Abstract

A systematic analysis of finite-size effects at interfacial phase transitions is presented. Both static and (model A) dynamic phenomena are considered in a cubic ${L}^{d\mathrm{\ensuremath{-}}1}$ geometry with periodic boundary conditions in the directions parallel to the interfaces, but with no restriction on the interface separation z\ensuremath{\in}[0,\ensuremath{\infty}). In contrast to bulk critical phenomena, the finite-size behavior is shown to be qualitatively different at coexistence (with h=0) and for finite values of the symmetry-breaking field h. In particular, it is shown that the static finite-size scaling functions are singular in the finite-size limit when h\ensuremath{\ne}0. At coexistence, there are exponentially long relaxation times for L\ensuremath{\gg}${\ensuremath{\xi}}_{?}$, where ${\ensuremath{\xi}}_{?}$ is the interfacial correlation length, and a crossover to quasi-one-dimensional diffusive growth in the finite-size limit.