Critical exponents of the O(N) model in the infrared limit from functional renormalization

Abstract

We determined the critical exponent $\nu$ of the scalar O(N) model with a strategy based on the definition of the correlation length in the infrared limit. The functional renormalization group treatment of the model shows that there is an infrared fixed point in the broken phase. The appearing degeneracy induces a dynamical length scale there, which can be considered as the correlation length. It is shown that the IR scaling behavior can account either for the Ising type phase transition in the 3-dimensional O(N) model, or for the Kosterlitz-Thouless type scaling of the 2-dimensional O(2) model.

final version, 7 pages 7 figures, to appear in Phys. Rev. D

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• Spontaneous symmetry breaking and optimization of functional renormalization group
• Critical exponents in quantum Einstein gravity
• Degeneracy induced scaling of the correlation length for periodic models
• $c$-function and central charge of the sine-Gordon model from the non-perturbative renormalization group flow
• The Numerically Optimized Regulator and the Functional Renormalization Group
• Asymptotic safety in the sine-Gordon model
• Quantum-classical transition in the Caldeira-Leggett model
• Tunable tachyon mass in the PT-broken massive Thirring model
• Perturbative versus Non-Perturbative Renormalization