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

Abstract 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 − e dimensions within the minimal subtraction scheme in the six-loop approximation. The e expansions for marginal dimensionalities of the order parameter n H ( m , 4 − e ) , n − ( m , 4 − e ) , n + ( m , 4 − e ) separating different regimes of critical behavior are extended up to e 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 e 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.