A Monte Carlo test of the Fisher–Nakanishi–Scaling theory for the capillary condensation critical point

Abstract

Extending the Swendsen–Wang cluster algorithm to include both bulk (H) and surface fields (H1) in L×L×D Ising films of thickness D and two free L×L surfaces, a Monte Carlo study of the capillary condensation critical point of the model is presented. Applying a finite-size scaling analysis where the lateral linear dimension L is varied over a wide range, the critical temperature Tc(D) and the associated critical field Hc(D) are estimated for 4⩽D⩽32 lattice spacings, for a choice of the surface field H1 small enough that the dependence of Hc(D) on H1 is still linear. It is shown that the results are consistent with the power laws predicted by Fisher and Nakanishi [M. E. Fisher and H. Nakanishi, J. Chem. Phys. 75, 5857 (1981)], namely Tc(∞)−Tc(D)∝D−1/ν, Hc(D)∝D−(Δ−Δ1)/ν, where ν is the bulk correlation length exponent of the three-dimensional Ising model, and Δ, Δ1 are the corresponding “gap exponents” associated with bulk and surface fields, respectively. As expected, the order parameter of the thin film near its critical point exhibits critical behavior compatible with the universality class of the two-dimensional Ising model.