Abstract

Starting from the 2-dimensional nonlinear ?-model living on a lattice ? of lattice spacing a with action S[?]=-12??z???, ?(z)?SN we compute a manifestly covariant closed form expression for the Wilson effective action Seff[?] on a lattice of lattice spacing ã in a 1-loop approximation for a Gaussian choice of blockspin, where C?(x)?C?(x)/|C?(x)| fluctuates around ?(x). C is averaging of ?(z) over a block x. The limiting case of a ?-function is also considered. The result extends Polyakov which had furnished those contributions to the effective action which are of order lnã/a. The additional terms which remain finite as a?0 include corrections other than coupling constant renormalization: a current-current interaction and a contribution from an augmented Jacobian which has a field dependence of a different kind than S has. Particular attention is paid to Seff's domain of validity in field space. It turns out that Hasenfratz and Niedermayer's choice of a low value of the parameter ? which governs the width of the Gaussian is optimal also in this respect. © 2001 Elsevier Science B.V.