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

TL;DR

This paper investigates the deconfinement transition in SU(2) gauge theory, analyzing critical couplings, scaling behavior, and continuum extrapolations, providing new insights into the theory's phase structure and comparisons with related models.

Contribution

It presents detailed scaling analysis and continuum extrapolations of critical couplings and ratios in SU(2) gauge theory, including comparisons with SU(3) and QCD.

Findings

Critical coupling for deconfinement transition determined.

Scaling of the ratio T_c / sqrt(σ) observed across coupling regime.

Continuum limit ratios T_c / Lambda_MS and sqrt(σ) / Lambda_MS obtained.

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.