Fluctuations and isentropes near the chiral critical endpoint

Isentropic trajectories crossing the chiral phase transition near the critical endpoint (CEP) are studied for two light quark flavors. The calculations are performed within an effective chiral model with quark-meson interactions, belonging to the same universality class as QCD. We confront mean-field thermodynamics with the functional renormalization group approach, where fluctuations are properly taken into account. We establish a connection between modifications of the isentropic trajectories found in mean-field calculations at the crossover transition near the CEP and the order of the phase transition in the chiral limit. Furthermore, the isentropes obtained with the renormalization group are completely smooth at the crossover transition and do not in any way reflect the proximity of the CEP. In particular, our results do not show the recently conjectured focussing of isentropes from the crossover region towards the critical endpoint.