Abstract
The critical behaviour of a semi-infiniten-vector model with a surface term (c/2) ∫d Sφ2 is studied in 4-ε dimensions near the special transition. It is shown that all critical surface exponents derive from bulk exponents and η∥, the anomalous dimension of the order parameter at the surface. The surface exponents and the crossover exponent Φ for the variablec are calculated to second order in ε. It is found that Φ does not satisfy the relation Φ=1-ν predicted by Bray and Moore. The order-parameter profilem(z)=<ø> is calculated to first order in ε. In contrast to mean-field theory,m(z) is not flat nor does it satisfy a Neumann boundary condition. General aspects of the field-theoretic renormalization program for systems with surfaces are discussed with particular attention paid to the explanation of the unfamiliar new features caused by the presence of surfaces.
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A brief account of some of the results presented here was given in [4]
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Diehl, H.W., Dietrich, S. Multicritical behaviour at surfaces. Z. Physik B - Condensed Matter 50, 117–129 (1983). https://doi.org/10.1007/BF01304094
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DOI: https://doi.org/10.1007/BF01304094