Functional renormalization group of the non-linear sigma model and the O(N) universality class

Abstract

We study the renormalization group flow of the O(N) non-linear sigma model in arbitrary dimensions. The effective action of the model is truncated to fourth order in the derivative expansion and the flow is obtained by combining the non-perturbative renormalization group and the background field method. We investigate the flow in three dimensions and analyze the phase structure for arbitrary N. The corresponding results about the critical properties of the models will serve as a reference for upcoming simulations with the Monte-Carlo renormalization group.

13 pages, 3 figures

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• Higher dimensional higher derivative ${\varphi }^4$ theory
• Asymptotic safety on the lattice: The Nonlinear O(N) Sigma Model
• Fluctuation-induced higher-derivative couplings and infrared dynamics of the Quark-Meson-Diquark Model
• Dynamically emergent gravity from hidden local Lorentz symmetry
• Functional renormalization of N scalars with O(N) invariance
• The Nordic-walking mechanism and its explanation of deconfined pseudocriticality from Wess-Zumino-Witten theory
• A different kind of four dimensional brane for string theory
• Renormalization of the Nonlinear O(3) Model with Theta-Term
• One-loop functional RG flow of scalar theory with electroweak symmetry
• Functional Renormalization Group Analysis of $O(3)$ Nonlinear Sigma Model and Non-Abelian Bosonization Duality
• Non-linear sigma models on constant curvature target manifolds: a functional renormalization group approach