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

DOI10.1016/J.NUCLPHYSB.2019.02.001zbMATH Open1409.81071arXiv1901.02754OpenAlexW2910929528MaRDI QIDQ1731685

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Publication date: 13 March 2019

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Abstract: The six-loop expansions of the renormalization-group functions of $varph{i}^4$ $n$-vector model with cubic anisotropy are calculated within the minimal subtraction (MS) scheme in $4-varepsilon$ 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 $n=3$.

Full work available at URL: https://arxiv.org/abs/1901.02754

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