Renormalization Group Ow and Xed Point of the Lattice Topological Charge in the 2{d O(3) {model Typeset Using Revt E X 2

We study the renormalization group evolution up to the xed point of the lattice topological susceptibility in the 2{d O(3) non{linear {model. We start with a discretization of the continuum topological charge by a local charge density, polynomial in the lattice elds. Among the diierent choices we propose also a Symanzik{improved lattice topological charge. We check step by step in the renormalization group iteration the progressive dumping of quantum uctuations, which are responsible for the additive and multiplicative renormalizations of the lattice topological susceptibility with respect to the continuum deenition. We nd that already after three iterations these renor-malizations are negligible and an excellent approximation of the xed point Work supported in part by Fondazione \A. Della Riccia" (Italy). 1 is achieved. We also check by an explicit calculation that the assumption of slowly varying elds in iterating the renormalization group does not lead to a good approximation of the xed point charge operator.