Five-loop epsilon expansion for O(n)xO(m) spin models
Pasquale Calabrese, Pietro Parruccini
Abstract
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(epsilon5). 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 re-analyzing 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+.
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