Five-loop ɛ expansion for O( n)× O( m) spin models

We compute the renormalization group functions of a Landau-Ginzburg-Wilson Hamiltonian with O( n)× 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 ɛ=4- d expansion for generic values of m up to O( ɛ⁵). 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- ɛ 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⁺.