  Extending the Swendsen-Wang cluster algorithm to include both bulk (H) and
surface fields (H_1) in L x L x D Ising films of thickness D and two free L x 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 T_c(D) and the associated critical field H_c(D) are estimated for 4
<= D <= 32 lattice spacings, for a choice of the surface field H_1 small enough
that the dependence of H_c(D) on H_1 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
T_c(\infty)-T_c(D) \propto D^{-1/\nu}, H_c(D) \propto D^{-(\Delta
-\Delta_1)/\nu}, where \nu is the bulk correlation length exponent of the
three-dimensional Ising model, and \Delta, \Delta_1 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.
