Five-loop ϵ expansion for O(n)×O(m) spin models Original Research Article

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 ϵ=4−d expansion for generic values of m up to O(ϵ5). 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-ϵ 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+.