INTERFACE LOCALIZATION TRANSITION IN ISING FILMS WITH COMPETING WALLS- GINZBURG CRITERION AND CROSSOVER SCALING

In a simple fluid or Ising magnet in a thin film geometry confined bet ween walls a distance D apart that exert opposing surface fields, an i nterface parallel to the walls is stabilized below the bulk critical t emperature T-cb. While this interface is ''delocalized'' (i.e., freely fluctuating in the center of the film) for T-cb > T > T-c(D), below t he ''interface localization transition' temperature T-c(D) the interfa ce is bound to one of the walls. Using the mean field description of P arry and Evans [Physica A 181, 250 (1992)], we develop a Ginzburg crit erion to show that the Ginzburg number scales exponentially with thick ness, Gi proportional to exp(-kappa D/2), kappa(-1) being the appropri ate 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 ve ry close neighborhood of T-c(D). A crossover scaling description is us ed 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 reana lyze 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 ed al. [Physica A 218, 77 (1995); 218, 109 (1995)] that the length scale kappa(-1) = e psilon(b)(1 + omega/2), where epsilon(b) is the true correlation range in the bulk, and omega is the universal amplitude associated with the interfacial stiffness.