Triangle Distribution and Equation of State for Classical Rigid Disks

Details Triangle Distribution and Equation of State for Classical Rigid Disks Triangle Distribution and Equation of State for Classical Rigid Disks

1999-10-27

arxiv.org/abs/cond-mat/9910451v1

Physics

Condensed Matter

Statistical Mechanics

40 pages, 8 Figures (To appear in the Journal of Statistical Physics)

Scientific paper

The triangle distribution function f^(3) for three mutual nearest 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 a unique f^(3) over the entire density range. The pressure equation of state exhibits qualitatively correct behavior 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.

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