Asymptotic freedom and mass generation in the O(3) nonlinear σ-model

Abstract

We complement a recently discovered collective Monte Carlo algorithm with a cluster variance reduction technique for the two-point function of σ-models. It is used to determine both the nonperturbative mass and the asymptotic freedom scale Λ MS from simulations of the O(3)-model with correlation lengths up to 121 on large lattices. We also estimate Λ MS in lattice units by studying the mass gap in physically small volumes. Asymptotic scaling with the bare coupling still does not occur. We propose an approximate lattice β-function that goes beyond finite-order perturbation theory and leads to better scaling behavior. The various methods give m/Λ MS = 2.5−3.0 for the O(3)-model.