$⟨A^2⟩$ asymmetry in lattice $SU(2)$ gluodynamics at $T>T_c$

We study numerically the chromoelectric-chromomagnetic asymmetry of the dimension two $A^2$ gluon condensate 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 the perturbative result.

Figure 1

Asymmetry on lattices $32^3\times 8$ as function of temperature. Lower dataset shows our results for first copy and should be compared with that obtained in [21]. Upper dataset was obtained with the FSA algorithm (best copy). The curves show results of the fits to Eq. (17).

Figure 2

Lattice size dependence of the asymmetry at $T/T_c=1.49$ (filled symbols) and 2.49 (empty symbols). Results are presented for $bc$ (squares), $fc$ (circles), and $wc$ (triangles). Curves show results of the fit to Eq. (20).

Figure 3

$bc$ results for the asymmetry normalized by its infinite volume value to compare finite volume effects at two temperatures, $T/T_c=1.49$ and 2.49. Curves show results of the fit to Eq. (20).

Figure 4

Relative deviation $D_{\text{flip}}$ for asymmetry, see Eq. (23) for definition. It demonstrates flip effects dependence on lattice size and temperature.

Figure 5

Asymmetry as function of the temperature for the fixed lattice size $L=2\mathrm{fm}$. The curves show the fit function (14) for $\xi >1.6$.

Figure 6

$\mathcal{A}$ for $bc$ for both $L=2\mathrm{fm}$ and $L=3\mathrm{fm}$. Curves show fits to the function (28).

Figure 7

$\mathcal{A}$ for all gauge-fixing procedures at $L=3\mathrm{fm}$. Curves show fits to the function (28).