A theory of the hard sphere solid. II
Abstract
A ''selfconsistent field'' theory based on the Bethe approximation previously estimated the entropy and singleparticle distribution function in good agreement with computer simulations for the threedimensional hardsphere solid. In this paper we carry through the theory for the hard disk system, finding results closely similar to those for hard spheres, and numerically in good agreement with asymptotic highdensity numerical simulations. Cluster corrections through thirdorder interactions are calculated and found small. The asymptotic highdensity approximation fails, correctly, to lead to a solution for the onedimensional system of rods in cells. In this case, an exact analytic solution is possible. For this solution, the oneparticle distribution function retains finite width in the highdensity limit, in contrast to the two and threedimensional solutions. At high densities, the free energy of this ''selfconsistent'' cell model solution corresponds to the known correct result.
 Publication:

Journal of Chemical Physics
 Pub Date:
 November 1975
 DOI:
 10.1063/1.431828
 Bibcode:
 1975JChPh..63.3870B
 Keywords:

 61.50.f;
 05.20.y;
 Crystalline state;
 Classical statistical mechanics