### Abstract

For various lattice gas models with nearest neighbor exclusion (and, in one case, second-nearest neighbor exclusion as well), we obtain lower bounds on m, the average number of particles on the nonexcluded lattice sites closest to a given particle. They are all of the form m/m_{cp}= 1 -const · (N_{cp}/N - 1), where N is the number of occupied sites, m_{cp} is the value of m at close packing, and N_{cp} is the value of N at close packing. An analogous result exists for hard disks in the plane.

Original language | English |
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Pages (from-to) | 89-95 |

Number of pages | 7 |

Journal | Journal of Statistical Physics |

Volume | 100 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 1 Jul 2000 |

### Keywords

- Close packing
- Hard disks
- Inequalities
- Lattice models
- Nearest neighbor exclusion

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## Cite this

Penrose, O., & Stell, G. (2000). Close to close packing.

*Journal of Statistical Physics*,*100*(1-2), 89-95. https://doi.org/10.1023/A:1018679309775