Abstract
For the title system the column-column transfer matrix is set up and diagonalized by exact calculation. The free energy and correlation length follow exactly from the eigenvalues of the auxiliary problem, whereas other quantities such as magnetization profiles, heat capacities, etc., are calculable numerically with arbitrary accuracy. The case of surface fields with the opposite signs is studied in some detail. The transition from exponentially decaying to oscillatory eigenvectors is discussed and related to wetting transitions. For the important case of the perfect asymmetry system the finite-size scaling near the wetting temperature ${\mathit{T}}_{\mathit{w}}$ of surface tension and correlation length parallel to the walls, is derived. Also the scaling of magnetization profiles is found. \textcopyright{} 1996 The American Physical Society.
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