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We study the renormalization group evolution up to the fixed point of thelattice topological susceptibility in the 2-d O(3) non-linear sigma-model. Westart with a discretization of the continuum topological charge by a localcharge density, polynomial in the lattice fields. Among the different choiceswe propose also a Symanzik--improved lattice topological charge. We check stepby step in the renormalization group iteration the progressive dumping ofquantum fluctuations, which are responsible for the additive and multiplicativerenormalizations of the lattice topological susceptibility with respect to thecontinuum definition. We find that already after three iterations theserenormalizations are negligible and an excellent approximation of the fixedpoint is achieved. We also check by an explicit calculation that the assumptionof slowly varying fields in iterating the renormalization group does not leadto a good approximation of the fixed point charge operator.Comment: 29 pages (25 PostScript file text + 4 PostScript figures); revised  version with new title, new abstract, added conclusions and other minor  change

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Renormalization group flow and fixed point of the lattice topological charge in the 2D O(3)<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math>model

Renormalization group flow and fixed point of the lattice topological charge in the 2D O(3)σmodel