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Phase Separation in the Neutral Falicov–Kimball Model

Authors
  • Kennedy, Tom
Type
Published Article
Journal
Journal of Statistical Physics
Publisher
Springer-Verlag
Publication Date
Jun 01, 1998
Volume
91
Issue
5-6
Pages
829–843
Identifiers
DOI: 10.1023/A:1023023230602
Source
Springer Nature
Keywords
License
Yellow

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.

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