1-Loop improved lattice action for the nonlinear σ-model

In this paper we show the Wilson effective action for the 2-dimensional O(N + 1)-symmetric lattice non-linear σ-model computed in the 1-loop approximation for the nonlinear choice of blockspin Φ(κ), Φ(κ) = Cφ(κ)/> Cφ(κ) parallel, where C is averaging of the fundamental field oe(z) over a square κ of side a-tilde. The result for Seff is composed of the classical perfect action with a renormalized coupling constant βeff, 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 a-tilde/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