Definition and statistical distributions of a topological number in the lattice O(3) sigma-model

We define a topological number Q for spin fields on a two-dimensional lattice. Q assumes integer values only and reduces to the well-known winding number in the classical continuum limit. A Monte Carlo measurement of the topological susceptibility chi1 = /volume on a 100 x 100 lattice reveals that it decreases exponentially with increasing β (= inverse bare coupling constant). The corresponding prediction of the perturbative renormalization group is not matched, however. (orig.)