2000/04/06 by Karl Haller, Haller, Karl, Tom Kennedy +1
Mathematics · Physics and Astronomy · #Astrophysics (astro-ph) #Condensed Matter (cond-mat) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Numerical methods for differential equations #Physics of Superconductivity and Magnetism #astro-ph #cond-mat #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.cond-mat/0004104
Latex, 22 pages, 12 postscript figures, to be submitted to J. Stat. Phys
arxiv created 2000/04/06 · openalex publication_date 2000/04/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the Falicov-Kimball model in two dimensions in the neutral case, i.e, the number of mobile electrons is equal to the number of ions. For rational densities between 1/3 and 2/5 we prove that the ground state is periodic if the strength of the attraction between the ions and electrons is large enough. The periodic ground state is given by taking the one dimensional periodic ground state found by Lemberger and then extending it into two dimensions in such a way that the configuration is constant along lines at a 45 degree angle to the lattice directions.