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

J. Fingberg; U. M. Heller; F. Karsch

doi:10.1016/0550-3213(93)90682-F

paper

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

arXiv:hep-lat/9208012 · doi:10.1016/0550-3213(93)90682-F

Abstract

We determine the critical couplings for the deconfinement phase transition in $S U (2)$ gauge theory on $N_{τ} \times N_{σ}^{3}$ lattices with $N_{τ} = 8$ and 16 and $N_{σ}$ varying between 16 and 48. A comparison with string tension data shows scaling of the ratio $T_{c} / σ$ in the entire coupling regime $β = 2.30 - 2.75$ , while the individual quantities still exhibit large scaling violations. We find $T_{c} / σ = 0.69 (2)$ . We also discuss in detail the extrapolation of $T_{c} / L amb d a_{M ˉ S ˉ}$ and $σ / L amb d a_{M ˉ S ˉ}$ to the continuum limit. Our result, which is consistent with the above ratio, is $T_{c} / L amb d a_{M ˉ S ˉ} = 1.23 (11)$ and $σ / L amb d a_{M ˉ S ˉ} = 1.79 (12)$ . We also comment upon corresponding results for $S U (3)$ gauge theory and four flavour QCD.

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.)

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The Running Coupling from Lattice Gauge Theory

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

Abstract

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