Abstract
The field theoretic renormalization-group approach for the study of critical behavior near free surfaces is generalized to dynamic properties. Time-dependent Ginzburg-Landau models with nonconserved or conserved order parameters — semi-infinite generalizations of the so-called modelsA andB — are considered. The asymptotic behavior of response and correlation functions is analyzed at the ordinary and special transitions in 4-ɛ dimensions, and dynamic scaling laws for surface quantities are obtained. It is shown that the critical exponents can be expressed entirely in terms of static bulk and surface exponents andz, the dynamic bulk exponent. The critical exponents for the leading frequency, temperature and momentum singularities of the surface two-spin correlation function at the ordinary transition differ appreciably from the corresponding bulk analogues. In addition, the shape function which describes its frequency dependence differs qualitatively from the one of the bulk correlation function.
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