Abstract
The Migdal-Kadanoff scheme is applied to the Ising model with a free surface. The resulting renormalization group transformation and the duality transformation commute in any dimension. Two simple recursion relations are obtained which reproduce the global phase diagram for the semi-infinite Ising model. The surface critical exponents calculated in this way are comparable to those obtained by more complex positionspace methods. In dimension d =2 + e', we find the exponents ~tl~sm--e' and y(hSm = 1 + e' for the multicritical surface-bulk transition. We also derive and discuss approximate differential recursion relations for the bulk and the surface free energies.
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