Finite-size scaling for critical films

Abstract

The universal scaling function of the fine-size contribution to the free energy of O(N) symmetric systems confined between two parallel plates at distance L is calculatd by field-theoretical methods close to ${\mathit{T}}_{\mathit{c},\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}}$ and for five different boundary conditions. The asymptotic behavior for large L of the specific heat at ${\mathit{T}}_{\mathit{c},}$b is computed explicitly, thus allowing quantitative experimental tests. We discuss the implications of our results for surface forces and wetting films. Universal amplitudes for the surface free energy are also presented.