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Thermodynamics and the phase structure of the Polyakov loop-extended twoflavors chiral quark--meson (PQM) model is explored beyond the mean-fieldapproximation. The analysis of the PQM model is based on the functionalrenormalization group (FRG) method. We formulate and solve the renormalizationgroup flow equation for the scale-dependent thermodynamic potential in thepresence of the gluonic background field at finite temperature and density. Wedetermine the phase diagram of the PQM model in the FRG approach and discussits modification in comparison with the one obtained under the mean-fieldapproximation. We focus on properties of the net-quark number densityfluctuations as well as their higher moments and discuss the influence ofnon-perturbative effects on their properties near the chiral crossovertransition. We show, that with an increasing net-quark number density thehigher order moments exhibit a peculiar structure near the phase transition. Wealso consider ratios of different moments of the net-quark number density anddiscuss their role as probes of deconfinement and chiral phase transitions.

The renormalization group and quark number fluctuations in the Polyakov loop extended quark-meson model at finite baryon density