1-loop improved lattice action for the nonlinear sigma-model

In this paper we show the Wilson effective action for the 2-dimensional O(N + 1)-symmetric lattice nonlinear sigma-model computed in the 1-loop approx imation for the nonlinear choice of blockspin Phi(x), Phi(x) = C phi(x)/\C phi(x)\,where C is averaging of the fundamental field phi(x) over a square x of side (a) over tilde. The result for S-eff is composed of the classical perfect action with a ren ormalized coupling constant beta(eff), an augmented contribution from a Jac obian, and further genuine 1-loop correction terms. Our result extends Poly akov's calculation which had furnished those contributions to the effective action which are of order ln (a) over tilde/a, where a is the lattice spac ing of the fundamental lattice. An analytic approximation for the backgroun d field which enters the classical perfect action will be presented elsewhe re [1].