We consider an Ising model confined in an $L\times \infty$ geometry with identical surface fields at the boundaries. According to the Kelvin equation the bulk coexistence field scales as $1/L$ for large $L;$ thermodynamics and scaling arguments predict higher-order corrections of the type ${1/L}^2$ and ${1/L}^{5/3}$ at partial and complete wetting, respectively. Our numerical results, obtained by density-matrix renormalization techniques for systems of widths up to $L=144,$ are in agreement with a ${1/L}^2$ correction in the partially wet regime. However, at complete wetting we find a large range of surface fields and temperatures with a correction to scaling of type ${1/L}^{4/3}.$ We show that this term is generated by a thin wetting layer whose free energy is dominated by the contacts with the wall. For $L$ sufficiently large we expect a crossover to a ${1/L}^{5/3}$ correction as predicted by the theory for a thick wetting layer. This crossover is indeed found in a solid-on-solid model, which provides a simplified description of the wetting layer and allows the study of much larger systems than those available in a density-matrix renormalization calculation.

• Received 16 March 1998

DOI:https://doi.org/10.1103/PhysRevB.58.5070