In a simple fluid or Ising magnet in a thin film geometry confined between walls a distance D apart that exert opposing surface fields, an interface parallel to the walls is stabilized below the bulk critical temperature T₂₁. While this interface is ``delocalized'' (i. e. , freely fluctuating in the center of the film) for T₂₁T₂ (D), below the ``interface localization transition'' temperature T₂ (D) the interface is bound to one of the walls. Using the mean field description of Parry and Evans Physica A 181, 250 (1992), we develop a Ginzburg criterion to show that the Ginzburg number scales exponentially with thickness, Gi (-/2), ^-1 being the appropriate transverse length scale associated with the interface. Therefore, mean field theory is self-consistent for large D, thus explaining why recent Monte Carlo simulations observed Ising criticality only in a very close neighborhood of T₂ (D). A crossover scaling description is used to work out the thickness dependence of the critical amplitudes in the Ising critical regime. Extending these concepts to consider finite size effects associated with the lateral linear dimension L, we reanalyze the Monte Carlo results of Binder, Landau, and Ferrenberg Phys. Rev. B 51, 2823 (1995). The data are in reasonable agreement with the theory, provided one accepts the suggestion of Parry et al. Physica A 218, 77 (1995) ; 218, 109 (1995) that the length scale ^-1=₁ (1+/2), where ₁ is the true correlation range in the bulk, and is the universal amplitude associated with the interfacial stiffness. 1996 The American Physical Society.
Binder et al. (Wed,) studied this question.