Anisotropic Improved Actions

Abstract

The studies of the quantum corrections for the anisotropy parameter,$η(=ξ_R/ξ_B)$, for the improved actions, $β(C_0 L({Plaq.}) + C_1 L({Rect.}))$, are proceeded in the medium to strong coupling region on anisotropic lattices. The global features for the $η$ parameters as a function of $β$ 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 $η(β)$ becomes less steep and for the actions whose $C_{1}$ is less than -0.160, $η$ decreases as $β$ decreases, contrary to the case of the standard action. In the medium to strong coupling region, the $η$ parameter begins to increase as $β$ decreases for all $C_{1}$. This means that for the actions with $C_{1} < -0.160$, the one-loop perturbative results for $η$ break down qualitatively and the $η$ parameters have a dip. As a result of this dip structure the $η$ for Iwasaki&#39;s action remains close to unity in the wide range of $β$.