### 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 |

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### Keywords

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

### Cite this

*Journal of Statistical Physics*,

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

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*Journal of Statistical Physics*, vol. 100, no. 1-2, pp. 89-95. https://doi.org/10.1023/A:1018679309775

**Close to close packing.** / Penrose, Oliver; Stell, George.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Close to close packing

AU - Penrose, Oliver

AU - Stell, George

PY - 2000/7/1

Y1 - 2000/7/1

N2 - 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/mcp= 1 -const · (Ncp/N - 1), where N is the number of occupied sites, mcp is the value of m at close packing, and Ncp is the value of N at close packing. An analogous result exists for hard disks in the plane.

AB - 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/mcp= 1 -const · (Ncp/N - 1), where N is the number of occupied sites, mcp is the value of m at close packing, and Ncp is the value of N at close packing. An analogous result exists for hard disks in the plane.

KW - Close packing

KW - Hard disks

KW - Inequalities

KW - Lattice models

KW - Nearest neighbor exclusion

UR - http://www.scopus.com/inward/record.url?scp=0034342323&partnerID=8YFLogxK

U2 - 10.1023/A:1018679309775

DO - 10.1023/A:1018679309775

M3 - Article

VL - 100

SP - 89

EP - 95

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-2

ER -