Six-loop $\epsilon$ expansion study of three-dimensional $O(n)\times O(m)$ spin models

Abstract

The Landau-Wilson field theory with $O(n)\times O(m)$ symmetry which describes the critical thermodynamics of frustrated spin systems with noncollinear and noncoplanar ordering is analyzed in $4-\epsilon$ dimensions within the minimal subtraction scheme in the six-loop approximation. The $\epsilon$ expansions for marginal dimensionalities of the order parameter $n^H(m,4-\epsilon )$, $n^{-}(m,4-\epsilon )$, $n^{+}(m,4-\epsilon )$ separating different regimes of critical behavior are extended up to ${\epsilon }^5$ terms. Concrete series with coefficients in decimals are presented for $m=\{2,\dots ,6\}$. The \textit{diagram of stability} of nontrivial fixed points, including the chiral one, in $(m,n)$ plane is constructed by means of summing up of corresponding $\epsilon$ 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.

References in corpus (8)

• Six-loop $\epsilon$ expansion study of three-dimensional $n$-vector model with cubic anisotropy
• Double phase transition in the triangular antiferromagnet Ba${}_3$CoTa${}_2$O${}_9$
• NaSrMn2F7, NaCaFe2F7, and NaSrFe2F7: novel single crystal pyrochlore antiferromagnets
• Spin Hamiltonian, {Order Out of a Coulomb Phase} and Pseudo-Criticality in the Highly Frustrated Pyrochlore Heisenberg Antiferromagnet FeF${}_3$}
• GraphState - a tool for graph identification and labelling
• Renormalization group functions of ${\varphi }^4$ theory in the MS-scheme to six loops
• The $3d$-Electron Heisenberg Pyrochlore Mn${}_2$Sb${}_2$O${}_7$
• Frustrated antiferromagnetic honeycomb-tunnel-like lattice CuRE2Ge2O8 (RE=Pr, Nd, Sm, and Eu)

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