MCRG Flow for the Nonlinear Sigma Model

Abstract

A study of the renormalization group flow in the three-dimensional nonlinear O(N) sigma model using Monte Carlo Renormalization Group (MCRG) techniques is presented. To achieve this, we combine an improved blockspin transformation with the canonical demon method to determine the flow diagram for a number of different truncations. Systematic errors of the approach are highlighted. Results are discussed with hindsight on the fixed point structure of the model and the corresponding critical exponents. Special emphasis is drawn on the existence of a nontrivial ultraviolet fixed point as required for theories modeling the asymptotic safety scenario of quantum gravity.

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

“…However, the MCRG method is more stable than the FRG method and leads to more robust results for different truncations. In particular, we do not find a sudden disappearance of the non-trivial fixed point for a certain truncation including the operator S 2 (28). Furthermore, we stress that lattice techniques provide the opportunity to obtain additional information beyond the chosen truncation by a direct measurement of the Green's functions.…”