# Phase Separation in the Neutral Falicov–Kimball Model

- Authors
- 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.