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The Wilson-Fisher ε expansion is used to calculate critical exponents in a semi-infinite Ising model to first order in ε. It is found that potentials renormalize just as in the bulk, and all surface information is contained in the wave-function renormalization. ν is 1/2+1/12ε and η is 0, just as in infinite systems. η_⊥ and η_∥ are, respectively, 1-1/6ε and 2-1/3ε and the surface gap exponent Δ₁ is 1/2-1/12ε if scaling is assumed.
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Lubensky et al. (1973) studied this question.
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