Near-critical confined fluids and Ising films: Density-matrix renormalization-group study

Two-dimensional Ising strips subject to identical surface fields h₁=h₂>~0 are studied for temperatures above and below the bulk critical temperature T_c and a range of bulk fields h by means of the density-matrix renormalization-group method. In the case of nonvanishing surface fields, the near-critical behavior of the solvation force f_solv, total adsorption Γ, inverse longitudinal correlation length ξ_‖^-1 and specific heat C_H is strongly influenced by the (pseudo) capillary condensation that occurs below T_c. We obtain scaling functions of f_solv, Γ, and ξ_‖^-1. C_H exhibits a weakly rounded singularity on crossing the pseudocoexistence line. We contrast these results with those for the case of free boundaries where, for temperatures slightly below T_c, f_solv and C_H exhibit a sharp extremum away from h=0. Our results have direct repercussions for the properties of near-critical Ising films in three dimensions and we argue that the long-ranged solvation (Casimir) force in confined fluids should be more attractive in the neighborhood of the capillary critical point than exactly at the bulk critical point.