We analyze the critical behavior of isotropic ferromagnets with a free surface by means of field-theoretic renormalization methods in d=2+{ε} dimensions. Renormalization-group equations for surface quantities are derived which imply scaling to all orders in {ε}. Explicit results to order ε² are presented for the critical surface exponents of the ordinary transition. Interpolation with the known results near four dimensions yields estimates for d=3 which seem to be remarkably accurate.
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Diehl et al. (1986) studied this question.
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