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

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

1999-09-23

arxiv.org/abs/hep-lat/9909149v1

Nucl.Phys.Proc.Suppl. 83 (2000) 881-883

Physics

High Energy Physics

High Energy Physics - Lattice

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

Scientific paper

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 $\Phi(x)$, $\Phi(x)= \Cav\phi(x)/{|\Cav\phi(x)|}$,where $\Cav$ is averaging of the fundamental field $\phi(z)$ 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.

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