Six-loop $\epsilon$ expansion study of three-dimensional $n$-vector model with cubic anisotropy

Abstract

The six-loop expansions of the renormalization-group functions of ${\phi }^4$ $n$-vector model with cubic anisotropy are calculated within the minimal subtraction (MS) scheme in $4-\epsilon$ dimensions. The $\epsilon$ expansions for the cubic fixed point coordinates, critical exponents corresponding to the cubic universality class and marginal order parameter dimensionality $n_c$ separating different regimes of critical behavior are presented. Since the $\epsilon$ 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 $n_c$ strengthens the existing arguments in favor of stability of the cubic fixed point in the physical case $n=3$.

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