Anisotropic Improved Actions

TL;DR

This paper investigates quantum corrections to the anisotropy parameter in improved lattice actions, revealing how the parameter behaves across different couplings and action coefficients, and identifying a dip structure for certain actions.

Contribution

It provides a detailed analysis of the anisotropy parameter's behavior for improved actions, including perturbative and non-perturbative features, especially for actions with varying coefficient C1.

Findings

The anisotropy parameter's slope decreases as C1 decreases.

For C1 less than -0.160, η decreases with decreasing β, contrary to standard actions.

A dip in η occurs for certain actions, keeping η close to unity over a wide range of β.

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 $\beta$.