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

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

1992-08-14

arxiv.org/abs/hep-lat/9208012v2

Nucl.Phys. B392 (1993) 493-517

Physics

High Energy Physics

High Energy Physics - Lattice

27 pages with 9 postscript figures included. Plain TeX file (needed macros are included). BI-TP 92-26, FSU-SCRI-92-103, HLRZ-9

Scientific paper

10.1016/0550-3213(93)90682-F

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 $T_c / Lambda_{\rm{\bar{M} \bar{S}}}$ and $\sqrt{\sigma} / Lambda_{\rm{\bar{M}\bar{S}}}$ to the continuum limit. Our result, which is consistent with the above ratio, is $T_c / Lambda_{\rm{\bar{M}\bar{S}}} = 1.23(11)$ and $\sqrt{\sigma} / Lambda_{\rm{\bar{M}\bar{S}}} = 1.79(12)$. We also comment upon corresponding results for $SU(3)$ gauge theory and four flavour QCD.

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