Gauge invariant study of the monopole condensation in non-Abelian lattice gauge theories

We investigate the Abelian monopole condensation in finite temperature SU(2) and SU(3) pure lattice gauge theories. To this end we introduce a gauge invariant disorder parameter built up in terms of the lattice Schrodinger functional. Our numerical results show that the disorder parameter is different from zero and Abelian monopoles condense in the confined phase. On the other hand, our numerical data suggest that the disorder parameter tends to zero, in the thermodynamic limit, when the gauge coupling constant approaches the critical deconfinement value. In the case of SU(3) we also compare the different kinds of Abelian monopoles which can be defined according to the choice of the Abelian subgroups.