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Advanced Statistical Mechanics$
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Barry M McCoy

Print publication date: 2009

Print ISBN-13: 9780199556632

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199556632.001.0001

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Ree–Hoover virial expansion and hard particles

Ree–Hoover virial expansion and hard particles

(p.181) 7 Ree–Hoover virial expansion and hard particles
Advanced Statistical Mechanics

Barry M. McCoy

Oxford University Press

This chapter derives the modification of the Mayer expansion made by Ree and Hoover. Analytic expressions for the virial coefficients B2,B3, and B4 are given and Monte–Carlo results for Bn for 5 ≤ n ≤ 10 in dimensions 1 ≤ D ≤ 10 are presented. Various approximate equations of state used to ‘fit’ these coefficients are summarized. Low order virial coefficients for hard squares, cubes and hexagons are given. Open questions relating to the signs of the virial coefficients for hard spheres and discs and to the relation of virial expansions to freezing are discussed.

Keywords:   hard discs, hard spheres, hard hexagons, Monte–Carlo evaluations, hard cubes, hard squares

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