Six-loop ε expansion study of three-dimensional O (n) x O (m) spin models

The Landau-Wilson field theory with O (n) x 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 s 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, ..., 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 s 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. (C) 2019 The Author(s). Published by Elsevier B.V.