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

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arxiv hep-lat/9208012 v2 pith:KDPSOLTX submitted 1992-08-14 hep-lat

classification hep-lat
keywords sigmalambdascalingsqrtgaugetheoryratioabove
verification ladder T0 review T1 audit T2 compute T3 formal
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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 $T_c / Lambda_{\rm{\bar{M} \bar{S}}}$ 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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Cited by 2 Pith papers

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    hep-lat 2025-09 accept novelty 6.0 of 10

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