GOLDSTONE BOSONS AND FINITE SIZE EFFECTS - A NUMERICAL STUDY OF THE O(4) MODEL

We study the 4-component PHI-4 model in 4 dimensions in the broken phase where the Goldstone modes dominate the finite size effects. Chiral perturbation theory relates the quantities measured at non-vanishing external source and in a finite volume to the low energy parameters-SIGMA (the field expectation value) and F (the pion decay constant) defined at infinite volume in the limit of vanishing external source. We analyze high statistics Monte Carlo data for the field expectation value and the Goldstone propagator by means of such expansions and we find very good agreement with the theoretically expected functional behaviour. It is possible to identify non-leading terms in the finite volume expansion and determine corresponding scale parameters. We also explore some alternative methods applicable at vanishing external source. Our analysis demonstrates that in a situation where the light Goldstone bosons control the dynamics of the system at large distances one may determine the infinite volume, zero external source quantities from finite volume simulations in a theoretically controlled way.