Abstract

In this paper we show the Wilson effective action for the 2-dimensional O(script N + 1)-symmetric lattice nonlinear ?-model computed in the 1-loop approximation for the nonlinear choice of blockspin ?(x), ?(x) = Cø(x) \Cø(x)\, where C is averaging of the fundamental field ø(z) over a square x of side ã. The result for Seff is composed of the classical perfect action with a renormalized coupling constant ?eff, an augmented contribution from a Jacobian, and further genuine 1-loop correction terms. Our result extends Polyakov's calculation which had furnished those contributions to the effective action which are of order ln ã a, where a is the lattice spacing of the fundamental lattice. An analytic approximation for the background field which enters the classical perfect action will be presented elsewhere [1].