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

Abstract

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 approximation for the nonlinear choice of blockspin $\Phi (x)$, $Φ(x)= \Cavϕ(x)/{|\Cavϕ(x)|}$,where $\Cav$ is averaging of the fundamental field $\varphi (z)$ over a square $x$ of side $\tilde{a}$. The result for $S_{eff}$ is composed of the classical perfect action with a renormalized coupling constant ${\beta }_{eff}$, 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 $\ln \tilde{a}/a$, 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.

3 (2-column format) pages, 1 tex file heplat99.tex, 1 macro package Espcrc2.sty To appear in Nucl. Phys. B, Proceedings Supplements Lattice 99

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• Analytic calculation of the 1-loop effective action for the O(N+1)-symmetric 2-dimensional nonlinear sigma-model