The critical behavior of a semi-infinite n-vector model in 4-ε dimensions near the special transition is studied. The renormalization of the relevant surface operators is discussed and explicitly carried out in two-loop order. It is found that the crossover exponent φₛ related to the square of the order parameter in the surface does not satisfy the relation φₛ=1-ν due to Bray and Moore.
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Diehl et al. (1981) studied this question.
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