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We study how the formalism of the Hierarchical Reference Theory (HRT) can beextended to inhomogeneous systems. HRT is a liquid state theory whichimplements the basic ideas of Wilson momentum shell renormalization group (RG)to microscopic Hamiltonians. In the case of homogeneous systems, HRT providesaccurate results even in the critical region, where it reproduces scaling andnon-classical critical exponents. We applied the HRT to study wetting criticalphenomena in a planar geometry. Our formalism avoids the explicit definition ofeffective surface Hamiltonians but leads, close to the wetting transition, tothe same renormalization group equation already studied by RG techiques.However, HRT also provides information on the non universal quantities becauseit does not require any preliminary coarse graining procedure. A simpleapproximation to the infinite HRT set of equations is discussed. The HRTevolution equation for the surface free energy is numerically integrated in asemi-infinite three-dimensional Ising model and the complete wetting phasetransition is analyzed. A renormalization of the adsorption critical amplitudeand of the wetting parameter is observed. Our results are compared to availableMonte Carlo simulations.Comment: To be published in Phy. Rev.

Microscopic approach to critical phenomena at interfaces: An application to complete wetting in the Ising model