Functional renormalization group of the nonlinear sigma model and the O(N) universality class

We study the renormalization group flow of the O(N) nonlinear 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 nonperturbative renormalization group and the background field method. We investigate the flow in three dimensions and analyze the phase structure for arbitrary N. While a nontrivial fixed point is present in a reduced truncation of the effective action and has critical properties that can be related to the well-known features of the O(N) universality class, one of the fourth-order operators destabilizes this fixed point and has to be discussed carefully. The results about the renormalization flow of the models will serve as a reference for upcoming simulations with the Monte Carlo renormalization group. DOI: 10.1103/PhysRevD.87.065019