Scaling and asymptotic scaling in the SU(2) gauge theory

Fingberg, J.; Heller, Urs M.; Karsch, F.

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

Scaling and asymptotic scaling in the SU(2) gauge theory

J. Fingberg
(
- Julich, NIC
)
,
Urs M. Heller
(
- Florida State U., SCRI
)
,
F. Karsch
(
- Julich, NIC and
- Bielefeld U.
)

Aug, 1992

27 pages

Published in:

Nucl.Phys.B 392 (1993) 493-517

e-Print:

hep-lat/9208012 [hep-lat]

DOI:

10.1016/0550-3213(93)90682-F

Report number:

FSU-SCRI-92-103,
BI-TP-92-26,
HLRZ-92-39

View in:

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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.

gauge field theory: SU(2)
gauge field theory: SU(3)
lattice field theory
critical phenomena
scaling: finite size
string tension
continuum limit
Polyakov loop
numerical calculations: Monte Carlo

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