Asymptotic safety on the lattice: The Nonlinear O(N) Sigma Model

Understand

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 $N$ 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.