  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.
