Multiple critical points in effective quark models

We consider the two-flavor version of the linear sigma model as well as of the Nambu--Jona-Lasinio model, at finite temperature and quark chemical potential, beyond the mean field approximation. Using parameter values for the pion and quark current masses which weakly break chiral symmetry, we show that both models can present more than one critical end point. In particular, we explicitly show that the appearance of a new critical point associated with a first-order line at high temperature and low densities could help to conciliate some lattice results with model predictions. Using different techniques, we perform an extensive thermodynamical analysis to understand the physical nature of the different critical points. For both models, our results suggest that the new first-order line which starts at vanishing chemical potential has a more chiral character than the usual line which displays a character more reminiscent of a liquid-gas phase transition.