Triangle Distribution and Equation of State for Classical Rigid Disks

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.

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Stillinger, D.K., Stillinger, F.H., Torquato, S. et al. Triangle Distribution and Equation of State for Classical Rigid Disks. Journal of Statistical Physics 100, 49–72 (2000). https://doi.org/10.1023/A:1018675208867

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  • rigid disks
  • packing
  • freezing transition
  • neighbor triangles