Computation of the Spatial String Tension in High Temperature SU(2) Gauge Theory

TL;DR

This paper investigates how the spatial string tension in high-temperature SU(2) gauge theory varies with temperature, demonstrating scaling behavior and providing a parametrization for temperatures above twice the critical temperature.

Contribution

It provides a detailed analysis of the temperature dependence of spatial string tension in SU(2) gauge theory, including scaling results and a new parametrization for high temperatures.

Findings

Spatial string tension remains constant below T_c.

Scaling of $\sigma_s$ observed between specific $eta$ values.

A parametrization of $\sigma_s(T)$ for T > 2T_c is proposed.

Abstract

A detailed investigation of the temperature dependence of the spatial string tension $\sigma_s$ in $SU(2)$ gauge theory is presented. A sustained performance of 3~GFLOPS on a 64K Connection Machine CM-2 equivalent has been achieved. Scaling of $\sigma_s$ between $\beta=2.5115$ and $\beta=2.74$, on large lattices, is demonstrated. Below the critical temperature, $T_c$, $\sigma_s$ remains constant. For temperatures larger than $2T_c$ the temperature dependence can be parametrized by $\sigma_s(T) = (0.369\pm 0.014)^2 g^4(T)T^2$, where $g(T)$ is a 2-loop running coupling constant with the scale parameter determined as $\Lambda_T = (0.076\pm 0.013)T_c$.