Five-loop \(\varepsilon\) expansion for \(O(n)\times O(m)\) spin models. (English) Zbl 1036.82506
Summary: We compute the renormalization group functions of a Landau-Ginzburg-Wilson Hamiltonian with \(O(n)\times O(m)\) 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 \(O(\varepsilon^5)\). 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 \(n>n^+\).
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 82B28 | Renormalization group methods in equilibrium statistical mechanics |
| 82B26 | Phase transitions (general) in equilibrium statistical mechanics |
| 82B27 | Critical phenomena in equilibrium statistical mechanics |
Keywords:
renormalization group functions; Landau-Ginzburg-Wilson Hamiltonian; second-order phase transition regionReferences:
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