Scaling and Asymptotic Scaling in the SU(2) Gauge Theory

Abstract

We determine the critical couplings for the deconfinement phase transition in $SU(2)$ gauge theory on $N_{\tau }\times N_{\sigma }^3$ lattices with $N_{\tau }=8$ and 16 and $N_{\sigma }$ varying between 16 and 48. A comparison with string tension data shows scaling of the ratio $T_c/\sqrt{\sigma }$ in the entire coupling regime $\beta =2.30-2.75$, while the individual quantities still exhibit large scaling violations. We find $T_c/\sqrt{\sigma }=0.69(2)$. We also discuss in detail the extrapolation of $T_c/Lambd{a}_{\bar{\mathrm{M}}\bar{\mathrm{S}}}$ and $\sqrt{\sigma }/Lambd{a}_{\bar{\mathrm{M}}\bar{\mathrm{S}}}$ to the continuum limit. Our result, which is consistent with the above ratio, is $T_c/Lambd{a}_{\bar{\mathrm{M}}\bar{\mathrm{S}}}=1.23(11)$ and $\sqrt{\sigma }/Lambd{a}_{\bar{\mathrm{M}}\bar{\mathrm{S}}}=1.79(12)$. We also comment upon corresponding results for $SU(3)$ gauge theory and four flavour QCD.

Comments: 27 pages with 9 postscript figures included. Plain TeX file (needed macros are included). BI-TP 92-26, FSU-SCRI-92-103, HLRZ-92-39 (Quote of UKQCD string tension, and accordingly Figs. 5 and 7a, plus a few typo's corrected.)