Five-loop ε expansion for O (n) X O (m) spin models

We compute the renormalization group functions of a Landau-Ginzburg-Wilson Hamiltonian with O(n) x O(m) symmetry up to five-loop in minimal subtraction scheme. The line n(+)(m, d), which limits the region of second-order phase transition, is reconstructed in the framework of the epsilon = 4 - d expansion for generic values of m up to O(epsilon(5)). For the physically interesting case of noncollinear but planar orderings (m = 2) we obtain n(+)(2, 3) = 6.1(6) by exploiting different resummation procedures. We substantiate this results reanalyzing six-loop fixed dimension series with pseudo-epsilon expansion, obtaining n(+)(2, 3) = 6.22(12). We also provide predictions for the critical exponents characterizing the second-order phase transition occurring for n > n(+). (C) 2003 Elsevier B.V. All rights reserved.