Surface critical behavior of semi-infinite systems with cubic anisotropy at the ordinary transition

Abstract

The critical behavior at the ordinary transition in semi-infinite n-component anisotropic cubic models is investigated by applying the field theoretic approach in d=3 dimensions up to the two-loop approximation. Numerical estimates of the resulting two-loop series expansions for the critical exponents of the ordinary transition are computed by means of Pade resummation techniques. For $n<n_{c}$ the system belongs to the universality class of the isotropic n-component model, while for $n>n_{c}$ the cubic fixed point becomes stable, where $n_{c}<3$ is the marginal spin dimensionality of the cubic model. The obtained results indicate that the surface critical behavior of the semi-infinite systems with cubic anisotropy is characterized by a new set of surface critical exponents for $n>n_{c}$.