Renormalization-group calculation of the critical properties of a free magnetic surface

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Abstract
A semi-infinite Ising model is studied by renormalization-group techniques in the position-space formulation due to Niemeijer and van Leeuwen. We show how to set up the calculation of thermodynamic properties (both critical and noncritical) of a sample with a free surface by iteration of a set of recursion relations for spatially inhomogeneous couplings and magnetic fields. Surface and bulk properties are clearly distinguished. The method is illustrated by a calculation (using a two-cell cluster approximation) of the magnetic-surface critical exponent in two dimensions, where exact results are available for comparison.