The topological structure of lattice gluodynamics is studied at intermediate resolution scale in the deconfining phase with the help of a cluster analysis. UV filtered topological charge densities are determined from a fixed number of low-lying eigen
modes of the overlap Dirac operator with three types of temporal boundary conditions applied to the valence quark fields. This method usually allows to find all three distinguished (anti)dyon constituents in the gauge field of Kraan-van Baal-Lee-Lu (anti)caloron solutions. The clustering of the three topological charge densities in Monte Carlo generated configurations is then used to mark the positions of anticipated (anti)dyons of the corresponding type. In order to support this interpretation, inside these clusters, we search also for time-like Abelian monopole currents (defined in the maximally Abelian gauge) as well as for local holonomies with at least two approximately degenerated eigenvalues. Our results support the view that light dyon-antidyon pairs - in contrast to the heavy (anti)caloron dyon constituents - contribute dominantly to thermal Yang-Mills fields in the deconfinement phase. This paper is dedicated to the memory of Pierre van Baal and Dmitri Igorevich Diakonov who have influenced our work very much.
The properties of the thermal Abelian color-magnetic monopoles in the maximally Abelian gauge are studied in the vicinity of the confinement-deconfinement phase transition in the lattice $SU(3)$ gluodynamics and lattice QCD. We compute the density an
d interaction parameters of the thermal monopoles. We find that the density of the thermal monopoles $rho(T)$ jumps up near the transition temperature $T_c$. Additionally we present new results on the percolation transition in $SU(3)$ gluodynamics which is known to coincide in gluodynamics with the confinement-deconfinement phase transition.
