Six-loop ε expansion study of three-dimensional n-vector model with cubic anisotropy

Abstract

The six-loop expansions of the renormalization-group functions of φ4n-vector model with cubic anisotropy are calculated within the minimal subtraction (MS) scheme in 4−ε dimensions. The ε expansions for the cubic fixed point coordinates, critical exponents corresponding to the cubic universality class and marginal order parameter dimensionality nc separating different regimes of critical behavior are presented. Since the ε expansions are divergent numerical estimates of the quantities of interest are obtained employing proper resummation techniques. The numbers found are compared with their counterparts obtained earlier within various field-theoretical approaches and by lattice calculations. In particular, our analysis of nc strengthens the existing arguments in favor of stability of the cubic fixed point in the physical case n=3.