# A Study of Finite Temperature Gauge Theory in (2+1) Dimensions

## TL;DR

This paper investigates the finite temperature phase transition in (2+1)-dimensional SU(2) and SU(3) gauge theories, determining critical parameters and string tension to understand their thermodynamic behavior.

## Contribution

It provides new measurements of critical couplings, exponents, and string tension in (2+1)D gauge theories, enhancing understanding of their finite temperature properties.

## Key findings

- Critical couplings and exponents determined for SU(2) and SU(3).
- Wilson loops measured at zero temperature with improved signal.
- Calculated ratio T_c/√σ to characterize the phase transition.

## Abstract

We determine the critical couplings and the critical exponents of the finite temperature transition in SU(2) and SU(3) pure gauge theory in (2+1) dimensions. We also measure Wilson loops at $T=0$ on a wide range of $\beta$ values using APE smearing to improve the signal. We extract the string tension $\sigma$ from a fit to large distances, including a string fluctuation term. With these two entities we calculate $T_c/\sqrt{\sigma}$.