Interacting ensemble of the instanton-dyons and the deconfinement phase transition in the SU(2) gauge theory

Instanton-dyons, also known as instanton-monopoles or instanton-quarks, are topological constituents of the instantons at nonzero temperature and holonomy. We perform numerical simulations of the ensemble of interacting dyons for the SU(2) pure gauge theory, using standard Metropolis Monte Carlo and integration over parameter methods. We calculate the free energy as a function of the holonomy (logarithm of the Polyakov line), the dyon densities, and the Debye mass, and find its minima as a function of those parameters. We show that the backreaction on the holonomy potential does generate confinement, provided the density is sufficiently high (or the temperature sufficiently low). We then report various properties of the self-consistent ensembles as a function of temperature.