Monte-Carlo simulations of QCD Thermodynamics in the PNJL model

We apply a Monte-Carlo method to the two flavor Polyakov loop extended Nambu and Jona-Lasinio (PNJL) model. In such a way we can go beyond mean field calculations introducing fluctuations of the fields. We study the impact of fluctuations on the thermodynamics of the model. We calculate the second derivatives of the thermodynamic grand canonical partition function with respect to the chemical potential and present a comparison with lattice data also for flavor non-diagonal susceptibilities.