Investigation of surface critical behavior of semi-infinite systems with cubic anisotropy

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The critical behavior at the special surface transition and crossover bevavior from special to ordinary surface transition in semi-infinite n-component anisotropic cubic models are investigated by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation. The crossover behavior for random semi-infinite Ising-like system, which is the nontrivial particular case of the cubic model in the limit n→ 0, is also investigated. The numerical estimates of the resulting two-loop series expansions for the critical exponents of the special surface transition, surface crossover critical exponent Φ and the surface critical exponents of the layer, α₁, and local specific heats, α₁₁, are computed by means of Pade and Pade-Borel resummation techniques. For n<nc the system belongs to the universality class of the isotropic n-component model, while for n>nc the cubic fixed point is stable, where nc is the marginal spin dimensionality of the cubic model. The obtained results indicate that the surface critical behavior of semi-infinite systems with cubic anisotropy is characterized by new set of surface critical exponents for n>nc.