Interacting instanton liquid in QCD at zero and finite temperatures

In this paper we study the statistical mechanics of the instanton liquid in QCD. After introducing the partition function as well as the gauge-field- and quark-induced interactions between instantons, we describe a method to calculate the free energy of the instanton system. We use this method to determine the equilibrium density and the equation of state from numerical simulations of the instanton ensemble in QCD for various numbers of flavors. We find that there is a critical number of flavors above which chiral symmetry is restored in the ground state. In the physical case of two light and one intermediate mass flavors, the system undergoes a chiral phase transition at $T\simeq 125$ MeV. We show that the mechanism for this transition is a rearrangement of the instanton liquid, going from a disordered, random phase at low temperatures to a strongly correlated, molecular phase at high temperature. We also study the behavior of mesonic susceptibilities near the phase transition.