Competing bulk and surface fields in d = 2 Ising films near bulk criticality: effects of fluctuations

The two-dimensional Ising films L x infinity with bulk H and surface H-1 fields of opposite sign are studied above and close to bulk criticality by the density matrix renormalization group method. This technique, applied recently to d = 2 Ising films, allows for very accurate results for the adsorption Gamma as a function of the reduced deviation from the critical temperature tau. For strong H1 three distinct classes of shapes of Gamma(tau), determined by the value of the parameter tau(H) similar to (\H\L)(1/(Delta-nu)), where L is the width of the film, are found in agreement with earlier predictions [A. Maciolek, A. Ciach, R. Evans, J. Chem. Phys. 108, 9765 (1998)]. For strong and for weak bulk fields Gamma(tau) is a monotonic function, increasing for strong H and decreasing for weak H, in agreement with scaling analysis and earlier mean-field results. For H between these extreme cases Gamma(tau) assumes a maximum for tau similar to tau(H) and for tau < tau(H) a depletion occurs, as in recent experiments for critical adsorption in porous materials. For a limited range of H a qualitatively new behavior of Gamma(tau) is found. In addition to a maximum, a minimum of Gamma( tau) for tau similar to L-1/nu < tau(H) appears, which in the mean-field analysis was absent.