# Scaling of the critical temperature and quark potential with a renormalization group improved SU(3) gauge action

## TL;DR

This paper investigates how the ratio of the critical temperature to the square root of the string tension scales in SU(3) gauge theory using an improved action, showing good scaling and rotational invariance.

## Contribution

It demonstrates the scaling behavior of T_c/√σ with a renormalization group improved SU(3) gauge action and compares it to the standard action, highlighting improved rotational invariance.

## Key findings

- T_c/√σ values are consistent in the infinite volume limit.
- Potential V(R) scales in physical units across the studied R range.
- Rotational invariance of the static quark potential is significantly restored.

## Abstract

We study the scaling property of the ratio of the critical temperature $T_c$ to the square root of the string tension $\sigma$ in the SU(3) pure gauge theory using a renormalization group improved action. We first determine the critical coupling $\beta_c$ on lattices with temporal extension $N_t=4$ and 6, and then calculate the static quark potential at the critical couplings on lattices at zero temperature. The values of $T_{c}/\sqrt{\sigma}$ in the infinite volume limit are identical within errors, while they are slightly larger than the value extrapolated to the continuum limit with the standard action. We also note that the rotational invariance of the static quark potential is remarkably restored in the both cases, and that the potential $V(R)$ in physical units scales in the whole region of $R$ investigated.