ASYMPTOTIC FREEDOM AND MASS GENERATION IN THE O(3) NONLINEAR SIGMA-MODEL

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 ΛMS from simulations of the O(3)-model with correlation lengths up to 121 on large lattices. We also estimate ΛMS 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/ΛMS= 2.5-3.0 for the O(3)-model. © 1990.