TESTING HALDANE CONJECTURE IN THE O(3) MODEL BY A MERON CLUSTER SIMULATION

Twelve years ago, Haldane formulated his famous conjecture for 1-d ant iferromagnetic quantum spin chains. In the context of the 2-d 0(3) sig ma model with a theta term, it predicts a phase transition as theta -- > pi, which has not yet been verified reliably. To simulate this we us e the Wolff cluster algorithm together with an improved estimator for the charge distribution. Each cluster carries integer or half integer charge. Clusters with charge 1/2 are identified with merons. At theta = pi they are inactive, such that the mass gap vanishes. We obtain cri tical exponents which are consistent with predictions from the k = 1 W ZNW model, therefore confirming a second order phase transition.