  Finite volume effects are studied both with low-momentum cutoff and with
momentum discretization in the framework of an (axial)vector meson extended
quark-meson model with Polyakov-loop variables. In the momentum cutoff
scenario, the CEP moves to lower temperatures and larger quark chemical
potentials as the characteristic system size is reduced, however, the treatment
of the vacuum term significantly affects its trajectory. The size dependence of
the baryon fluctuations is also studied by the kurtosis and the skewness, both
of which show moderate dependence on temperature and some dependence on quark
chemical potential. The order of the phase transition is also studied near the
chiral limit at finite system size and found to be second-order only at
vanishing explicit breaking. The implementation of the finite size effect with
momentum discretization is more complicated and shows peculiar behavior due to
the different modes dropping below the Fermi surface and strong dependence on
the type of the boundary condition chosen. We found that both the different
boundary conditions and the treatment of the vacuum term cause significant
changes in the trajectory of the CEP as the characteristic system size is
changed.
