Anisotropic Improved Actions

Abstract

The studies of the quantum corrections for the anisotropy parameter,$\eta (={\xi }_R/{\xi }_B)$, for the improved actions, $\beta (C_{0}L(Plaq.)+C_{1}L(Rect.))$, are proceeded in the medium to strong coupling region on anisotropic lattices. The global features for the $\eta$ parameters as a function of $\beta$ and the coefficient $C_1$ have been clarified. It has been found by the perturbative analysis that as $C_1$ decreases, the slope of the $\eta (\beta )$ becomes less steep and for the actions whose $C_1$ is less than -0.160, $\eta$ decreases as $\beta$ decreases, contrary to the case of the standard action. In the medium to strong coupling region, the $\eta$ parameter begins to increase as $\beta$ decreases for all $C_1$. This means that for the actions with $C_1<-0.160$, the one-loop perturbative results for $\eta$ break down qualitatively and the $\eta$ parameters have a dip. As a result of this dip structure the $\eta$ for Iwasaki's action remains close to unity in the wide range of $\beta$.

Comments: LATTICE99(hightemp), 3 pages in latex, 4 Postscript figures