Phase separation in the neutral Falicov-Kimball model

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25 Scopus citations

Abstract

The Falicov-Kimball model consists of spinless electrons and classical particles (ions) on a lattice. The electrons hop between nearest neighbor sites, while the ions do not. We consider the model with equal numbers of ions and electrons and with a large on-site attractive force between ions and electrons. For densities 1/4 and 1/5, the ion configuration in the ground state had been proved to be periodic. We prove that for density 2/9 it is periodic as well. However, for densities between 1/4 and 1/5 other than 2/9 we prove that the ion configuration in the ground state is not periodic. Instead there is phase separation. For densities in (1/5, 2/9) the ground-state ion configuration is a mixture of the density 1/5 and 2/9 ground-state ion configurations. For the interval (2/9, 1/4) it is a mixture of the density 2/9 and 1/4 ground states.

Original languageEnglish (US)
Pages (from-to)829-843
Number of pages15
JournalJournal of Statistical Physics
Volume91
Issue number5-6
DOIs
StatePublished - Jun 1998

Keywords

  • Falicov-kimball model
  • Ground state
  • Phase separation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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