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

TL;DR

This study investigates the surface critical behavior of semi-infinite systems with cubic anisotropy using field theory, revealing new surface critical exponents for systems with n greater than the marginal spin dimensionality.

Contribution

It provides the first detailed two-loop field theoretic analysis of surface critical behavior in cubic anisotropic models in three dimensions, including crossover phenomena and numerical estimates of critical exponents.

Findings

Surface critical exponents are computed for different n values.

New surface critical exponents are identified for n > n_c.

Crossover behavior from special to ordinary surface transition is characterized.

Abstract

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 $n\to 0$, 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 $\Phi$ and the surface critical exponents of the layer, $\alpha_{1}$, and local specific heats, $\alpha_{11}$, are computed by means of Pade and Pade-Borel 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 is stable, where $n_{c}$ 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 $n>n_{c}$.