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

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 ${\Lambda }_T=(0.076\pm 0.013)T_c$.

(Minor changes: Postscript format, typos corrected, language and grammar improved, formula (5) corrected, 1 new citation), 15 pages, 6 figures, postscript (480K)