Abstract
The 1/ n expansion method is developed in the study of the critical behavior of the n-vector model with a free surface. The method is applied at the bulk critical temperature (T = Tc) in the absence of the surface ordering. The surface critical exponents Till and Til. are identified up to order 1/ n for general spatial dimension d: 2< d < 4 for the ordinary transition and 3 < d < 4 for the special transition. The results are compared with several scaling relations, other theories and some experiments.
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