  We consider prescriptions that are free from the direct charge-screening
effects by quark loops and enable us to clarify the confining nature of a
vacuum. We test two candidates for an order parameter, a Polyakov loop ($P$)
evaluated in zero-triality backgrounds and fermionic determinants (${\mathcal
D}_{1,2}$) with non-zero triality. Especially, ${\mathcal D}_{1,2}$ has very
small fluctuations in comparison with a Polyakov loop in zero-triality sector,
and seems to well reflect the characteristic of a vacuum. Such prescriptions
could be still usable for the clarification of the confinement property of a
vacuum.

High Energy Physics - Lattice