  We analyze the thermodynamic properties of interfaces in the
three-dimensional Falicov Kimball model, which can be viewed as a primitive
quantum lattice model of crystalline matter. In the strong coupling limit, the
ionic subsystem of this model is governed by the Hamiltonian of an effective
classical spin model whose leading part is the Ising Hamiltonian. We prove that
the 100 interface in this model, at half-filling, is rigid, as in the
three-dimensional Ising model. However, despite the above similarities with the
Ising model, the thermodynamic properties of its 111 interface are very
different. We prove that even though this interface is expected to be unstable
for the Ising model, it is stable for the Falicov Kimball model at sufficiently
low temperatures. This rigidity results from a phenomenon of "ground state
selection" and is a consequence of the Fermi statistics of the electrons in the
model.
