Free energy behavior in exactly solvable many-fermion interacting systems

The objective of this work is to show that simple modifications in the form of the fermion-fermion interacting potential generate widely different thermodynamic behaviors, with macroscopic manifestations reflected by the thermal free energy. This is done by appealing to quantum statistical mechanics, in its Gibbs' ensemble formalism, employing two different SU2 exactly solvable models. Some intriguing aspects of the fermion dynamics are uncovered. We conclude that, in investigating fermion dynamics, minute changes in the Hamiltonian may lead to dramatic consequences in the behavior of the Helmholtz' free energy.