On a projection in dependence on monopole condensate in the lattice SU(2) gauge theory

We study the temperature dependence of the monopole condensate in different Abelian projections of the SU(2) lattice gauge theory in the thermodynamic limit. Using the Fröhlich-Marchetti monopole creation operator, we show numerically that the monopole condensate depends strongly on the choice of the Abelian projection. Contrary to the claims in the literature, we observe that, in the Abelian-Polyakov gauge and in the field strength gauge, the monopole condensate does not vanish at the critical temperature in the large-volume limit. Therefore, the monopole condensate in these gauges is not an order parameter of the confinement-deconfinement phase transition.