## Abstract

The triangle distribution function f^{(3)} for three mutual near neighbors in the plane describes basic aspects of short-range order and statistical thermodynamics in two-dimensional many-particle systems. This paper examines prospects for constructing a self-consistent calculation for the rigid-disk-system f^{(3)}. We present several identities obeyed by f^{(3)}. A rudimentary closure suggested by scaled-particle theory is introduced. In conjunction with three of the basic identities, this closure leads to an unique f^{(3)} over the entire density range. The pressure equation of state exhibits qualitatively correct behaviors in both the low-density and the close-packed limits, but no intervening phase transition appears. We discuss extensions to improved disk closures, and to the three-dimensional rigid-sphere system.

Original language | English (US) |
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Pages (from-to) | 49-72 |

Number of pages | 24 |

Journal | Journal of Statistical Physics |

Volume | 100 |

Issue number | 1-2 |

DOIs | |

State | Published - Jul 2000 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Keywords

- Freezing transition
- Neighbor triangles
- Packing
- Rigid disks