The $A^2$ asymmetry and propagators in lattice $SU(2)$ gluodynamics at $T>T_c$

TL;DR

This study investigates the behavior of the $A^2$ gluon condensate asymmetry and gluon propagators in lattice $SU(2)$ gauge theory at temperatures above the critical temperature, revealing finite-volume effects and proposing a new indicator for the postconfinement boundary.

Contribution

The paper demonstrates that the symmetric point of asymmetry change is an artifact of finite-volume effects and introduces the ratio of transverse to longitudinal propagators as a new boundary indicator.

Findings

Asymmetry decreases with temperature, approaching zero from above.

Finite-volume effects influence the observed symmetric point.

The ratio of propagators indicates the postconfinement boundary at approximately 1.7 times $T_c$.

Abstract

We study numerically the chromoelectric-chromomagnetic asymmetry of the dimension two $A^2$ gluon condensate as well as the transverse and longitudinal gluon propagators at $T>T_c$ in the Landau-gauge $SU(2)$ lattice gauge theory with a particular emphasis on finite-volume effects. We show that previously found so called symmetric point at which asymmetry changes sign is an artifact of the finite volume effects. We find that with increasing temperature the asymmetry decreases approaching zero value from above in agreement with perturbative result. Instead of the asymmetry we suggest the ratio of the transverse to longitudinal propagator taken at zero momentum as an indicator of the boundary of the postconfinement domain and find it at $T \simeq 1.7 T_c$.