Finite-size scaling in layered systems with surface ordering

Motivated by recent experiments on liquid-crystal films, we study finite-size scaling of a layered system in the presence of surface ordering. We find that there is an important length scale Ξs, characterizing the decay of surface order into the bulk. The usual finite-size scaling is generalized by including n/Ξs as an additional scaling variable, with n the number of layers. The bulk transition temperature is governed by a new scaling function Fs(n/Ξs), which decreases with n for n < Ξs, but increases with n for n >Ξs. Qualitative trends agree well with the experiments.