Massive field-theory approach to surface critical behavior in three-dimensional systems

The massive field-theory approach for studying critical behavior in fixed space dimensions d < 4 is extended to systems with surfaces. This enables one to study the surface critical behavior directly in dimensions d < 4 without having to resort to the epsilon expansion. The approach is elaborated for the representative case of the semi-infinite \phi\(4) n-vector model with a boundary term 1/2 c(0) integral(partial derivative v) phi(2) in the action. To make the theory UV finite in bulk dimensions 3 less than or equal to d < 4, a renormalization of the surface enhancement co is required in addition to the standard mass renormalization. Adequate normalization conditions for the renormalized theory are given. This theory involves two mass parameters: the usual bulk 'mass' (inverse correlation length) m, and the renormalized surface enhancement c. Thus the surface renormalization factors depend on the renormalized coupling constant u and the ratio c/m. The special and ordinary surface transitions correspond to the limits m --> 0 with c/m --> 0 and c/m --> infinity, respectively. It is shown that the surface-enhancement renormalization turns into an additive renormalization in the limit c/m --> infinity. The renormalization factors and exponent functions with c/m = 0 and c/m = infinity that are needed to determine the surface critical exponents of the special and ordinary transitions are calculated to two-loop order at d = 3. The associated series expansions are analyzed by Pade-Borel summation techniques. The resulting numerical estimates for the surface critical exponents are in good agreement with recent Monte Carlo data. This is also true for the surface crossover exponent Phi, for which we obtain Phi(n = 0) similar or equal to 0.52 and Phi (n = 1) similar or equal to 0.54, values considerably lower than the previous epsilon-expansion estimates. (C) 1998 Elsevier Science B.V.