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Blaizot, Jean-Paul; Méndez-Galain, Ramón; Wschebor, Nicolás

A new method to solve the non-perturbative renormalization group equations. (English) Zbl 1247.81308

Phys. Lett., B 632, No. 4, 571-578 (2006).
Summary: We propose a method to solve the non-perturbative renormalization group equations for the \(n\)-point functions. In leading order, it consists in solving the equations obtained by closing the infinite hierarchy of equations for the \(n\)-point functions. This is achieved: (i) by exploiting the decoupling of modes and the analyticity of the \(n\)-point functions at small momenta: this allows us to neglect some momentum dependence of the vertices entering the flow equations; (ii) by relating vertices at zero momenta to derivatives of lower order vertices with respect to a constant background field. Although the approximation is not controlled by a small parameter, its accuracy can be systematically improved. When it is applied to the \(O(N)\) model, its leading order is exact in the large-\(N\) limit; in this case, one recovers known results in a simple and direct way, i.e., without introducing an auxiliary field.

Cited in 15 Documents

MSC:

81T17 Renormalization group methods applied to problems in quantum field theory

Keywords:

non-perturbative renormalization group equations
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\textit{J.-P. Blaizot} et al., Phys. Lett., B 632, No. 4, 571--578 (2006; Zbl 1247.81308)
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