Six-loop \(\varepsilon\) expansion study of three-dimensional \(\mathrm{O}(n) \times \mathrm{O}(m)\) spin models

DOI10.1016/J.NUCLPHYSB.2019.114874zbMATH Open1482.82022arXiv1911.01091OpenAlexW2990332097MaRDI QIDQ2230124

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Publication date: 17 September 2021

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Abstract: The Landau-Wilson field theory with $O(n)imesO(m)$ symmetry which describes the critical thermodynamics of frustrated spin systems with noncollinear and noncoplanar ordering is analyzed in $4-varepsilon$ dimensions within the minimal subtraction scheme in the six-loop approximation. The $varepsilon$ expansions for marginal dimensionalities of the order parameter $n^H(m,4-varepsilon)$, $n^{-}(m,4-varepsilon)$, $n^{+}(m,4-varepsilon)$ separating different regimes of critical behavior are extended up to $varepsilo{n}^5$ terms. Concrete series with coefficients in decimals are presented for $m=2,dots,6$. The extit{diagram of stability} of nontrivial fixed points, including the chiral one, in $(m,n)$ plane is constructed by means of summing up of corresponding $varepsilon$ expansions using various resummation techniques. Numerical estimates of the chiral critical exponents for several couples $m,n$ are also found. Comparative analysis of our results with their counterparts obtained earlier within the lower-order approximations and by means of alternative approaches is performed. It is confirmed, in particular, that in physically interesting cases $n=2,m=2$ and $n=2,m=3$ phase transitions into chiral phases should be first-order.

Full work available at URL: https://arxiv.org/abs/1911.01091

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