Rigidity of Interfaces in the Falicov–Kimball Model

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.