  We study the finite temperature properties of two-component fermionic atoms
trapped in a two-dimensional optical lattice. We apply the self-energy
functional approach to the two-dimensional Hubbard model with a harmonic
trapping potential, and systematically investigate the thermodynamic properties
of this system. We find that entropy and grand potential provide evidence of a
crossover between the Mott insulating and metallic phases at certain
temperatures. In addition, we find that entropy exhibits a cusp-like anomaly at
lower temperatures, suggesting a second or higher order antiferromagnetic
transition. We estimate the antiferromagnetic transition temperatures, and
clarify how the trapping potential affects this magnetic transition.
