Finite temperature and density in non-local chiral quark models

Chiral quark models with non-local covariant separable interactions at finite temperature and chemical potential are investigated. We develop a formalism in which the different quark properties are evaluated taking into account the analytic structure of the quark propagator. In this framework we study the chiral restoration phase transition for some definite non-local regulators. We find that in all cases the chiral transition is of first order for low values of T, turning into a smooth crossover at a certain "end point". Using model parameters which lead to the physical pion mass and decay constant, we find for the position of this "end point" the values (T-E, mu(E)) approximate to (60 - 701180 - 210) MeV.