Nilanjana Datta, Alain Messager, Bruno Nachtergaele
Rigidity of interfaces in the Falicov-Kimball model
(332K, LATeX 2e)
ABSTRACT. 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.