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

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The ratios R 2k of renormalized coupling constants g 2k that enter the effective potential and smallfield equation of state acquire the universal values at criticality. They are calculated for the three-dimensional scalar λφ 4 field theory (3D Ising model) within the pseudo-expansion approach. Pseudo-expansions for the critical values of g 6 , g 8 , g 10 , R 6 = g 6 /g 2 4 , R 8 = g 8 /g 3 4 and R 10 = g 10 /g 4 4 originating from the five-loop renormalization group (RG) series are derived. Pseudo-expansions for the sextic coupling have rapidly diminishing coefficients, so addressing Padé approximants yields proper numerical results. Use of Padé-Borel-Leroy and conformal mapping resummation techniques further improves the accuracy leading to the values R * 6 = 1.6488 and R * 6 = 1.6490 which are in a brilliant agreement with the result of advanced lattice calculations. For the octic coupling the numerical structure of the pseudo-expansions is less favorable. Nevertheless, the conform-Borel resummation gives R * 8 = 0.868, the number being close to the lattice estimate R * 8 = 0.871 and compatible with the result of 3D RG analysis R * 8 = 0.857. Pseudo-expansions for R * 10 and g * 10 are also found to have much smaller coefficients than those of the original RG series. They remain, however, fast growing and big enough to prevent obtaining fair numerical estimates.