4 years ago

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

L.ts. Adzhemyan, E.v. Ivanova, M.v. Kompaniets, A. Kudlis, A.i. Sokolov

The six-loop expansions of the renormalization-group functions of $\varphi^4$ $n$-vector model with cubic anisotropy are calculated within the minimal subtraction (MS) scheme in $4 - \epsilon$ dimensions. The $\varepsilon$ 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 $\varepsilon$ 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 $n = 3$.

Publisher URL: http://arxiv.org/abs/1901.02754

DOI: arXiv:1901.02754v1

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