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The critical region of the two flavour quark-meson model with vectorinteractions is explored using the Functional Renormalization Group technique,a non-perturbative method that takes into account quantum and thermalfluctuations. Special attention is given to the low temperature and highdensity region of the phase diagram, which is very important for the evolutionof proto-neutron stars and to construct the equation of state of compact stars.As in previous studies, without repulsive vector interaction, an unphysicalregion of negative entropy density is found near the first order chiral phasetransition. We explore the connection between this unphysical region and thechiral critical region, especially the first order line and spinodal lines,using also different values for vector interactions. The effect of finitevector interactions in the critical region is explored. We find that theunphysical negative entropy density region appears because the $s=0$ isentropicline, near the critical region, is displaced from its $T=0$ location. Forcertain values of vector interactions this region is pushed to lowertemperatures and high chemical potentials in such way that the negative entropydensity region on the phase diagram of the model can even disapear. In the caseof finite vector interactions, the location of the critical end point has anon-trivial behaviour in the $T-\mu_B$ plane, which differs from that inmean-field calculations.

Functional renormalization group study of the critical region of the quark-meson model with vector interactions