Asymptotic safety on the lattice: The nonlinear O(N) sigma model

• We compute the global flow diagram from lattice simulations.
• Truncation of the effective action may lead to artificial fixed points.
• Our optimization scheme effectively reduces truncation errors.
• The Wilson–Fisher fixed point is identified as a non-trivial UV fixed point.
• Asymptotic safety is realized for the 3D nonlinear sigma model.

We study the non-perturbative renormalization group flow of the nonlinear O(N) sigma model in two and three spacetime dimensions using a scheme that combines an effective local Hybrid Monte Carlo update routine, blockspin transformations and a Monte Carlo demon method. In two dimensions our results verify perturbative renormalizability. In three dimensions, we determine the flow diagram of the theory for various NN and different truncations and find a non-trivial fixed point, which indicates non-perturbative renormalizability. It is related to the well-studied phase transition of the O(N) universality class and characterizes the continuum physics of the model. We compare the obtained renormalization group flows with recent investigations by means of the Functional Renormalization Group.