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

Extending the Swendsen-Wang cluster algorithm to include both bulk (H) and surface fields (H-1) in LxLxD Ising films of thickness D and two free LxL s urfaces, a Monte Carlo study of the capillary condensation critical point o f the model is presented. Applying a finite-size scaling analysis where the lateral linear dimension L is varied over a wide range, the critical tempe rature T-c(D) and the associated critical field H-c(D) are estimated for 4 less than or equal toD less than or equal to 32 lattice spacings, for a cho ice 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 p ower laws predicted by Fisher and Nakanishi [M. E. Fisher and H. Nakanishi, J. Chem. Phys. 75, 5857 (1981)], namely T-c(infinity)-T-c(D)proportional t oD(-1/nu), H-c(D)proportional toD(-(Delta-Delta1)/nu), where nu is the bulk correlation length exponent of the three-dimensional Ising model, and Delt a, 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 th e universality class of the two-dimensional Ising model. (C) 2001 American Institute of Physics.