Chiral symmetry in the low-energy limit of QCD at finite temperature

We derive a nonlocal Nambu-Jona-Lasinio model from QCD with a form factor exactly obtained in the infrared limit. Using this model, with all parameters properly fixed via QCD, we consider the case of finite temperature and compute the solution of the gap equation at low temperature, small momentum, and zero chemical potential. Taking the quark masses to be zero, we prove that the theory undergoes a phase transition with a critical temperature that is exactly determined. These results prove unequivocally that the picture of the vacuum of QCD as a liquid of instantons is a very good approximation.