  Thermodynamics and the phase structure of the Polyakov loop-extended two
flavors chiral quark--meson (PQM) model is explored beyond the mean-field
approximation. The analysis of the PQM model is based on the functional
renormalization group (FRG) method. We formulate and solve the renormalization
group flow equation for the scale-dependent thermodynamic potential in the
presence of the gluonic background field at finite temperature and density. We
determine the phase diagram of the PQM model in the FRG approach and discuss
its modification in comparison with the one obtained under the mean-field
approximation. We focus on properties of the net-quark number density
fluctuations as well as their higher moments and discuss the influence of
non-perturbative effects on their properties near the chiral crossover
transition. We show, that with an increasing net-quark number density the
higher order moments exhibit a peculiar structure near the phase transition. We
also consider ratios of different moments of the net-quark number density and
discuss their role as probes of deconfinement and chiral phase transitions.
