Flux phase problem in the 2-D Falicov-Kimball model

A lattice system of electrons in the presence of an external potential and under the influence of a magnetic field is considered. The energy of the electrons is given by the Falicov-Kimball hamiltonian, where the ions give the external potential. The problem is to find the configurations of ions and the magnetic fluxes which minimize the energy of the electrons at zero temperature. Our results, valid for large coupling constant, show that periodic configurations with periodic fluxes (possibly inhomogeneous) appear for some values of the chemical potentials