  In the experimental context of cold-fermion optical lattices, we discuss the
possibilities to approach the pseudogap or ordered phases by manipulating the
scattering length or the strength of the laser-induced lattice potential. Using
the Two-Particle Self-Consistent Approach as well as Quantum Monte Carlo
simulations, we provide isentropic curves for the two- and three-dimensional
Hubbard models at half-filling. These quantitative results are important for
practical attempts to reach the ordered antiferromagnetic phase in experiments
on optical lattices of two-component fermions. We find that adiabatically
turning on the interaction in two dimensions to cool the system is not very
effective. In three dimensions, adiabatic cooling to the antiferromagnetic
phase can be achieved in such a manner although the cooling efficiency is not
as high as initially suggested by Dynamical Mean-Field Theory. Adiabatic
cooling by turning off the repulsion beginning at strong coupling is possible
in certain cases.
