TOPOLOGICAL SUSCEPTIBILITY ON THE LATTICE - THE 2-DIMENSIONAL O(3) SIGMA-MODEL

As a test of the procedures used in lattice gauge theories, we study the topological susceptibility chi in a two-dimensional O(3) sigma or CP1 model. We determine chi by defining the density of topological charge as a local operator on the lattice. Following the prescriptions of field theory we perform the additive and multiplicative renormalizations needed to extract chi from Monte Carlo data. We also determine chi by the cooling method, finding consistent results. A combined use of cooling and field theory again gives the same result and insight into the renormalization mechanism. Finally we give a direct determination, by Monte Carlo techniques, of both the multiplicative and additive renormalizations, by heating configurations with a definite number of instantons. The results are consistent with perturbation theory.