EQUATION OF STATE OF THE HARD-DISC SOLID

We present a study of the equation of state of the hard-disc solid, in cluding the freezing transition. The: study is based on a weighted-den sity approximation scheme for the free-energy density functional of ha rd discs. Using a standard procedure to construct such a functional in terms of a suitably chosen weighting function, augmented to include a cubic (rather than quadratic) approximation fur the density dependenc e of the latter, we obtain the equation of state of the solid and use it to locate the densities where solid and fluid coexist. The equation of state is compared with constant-pressure Monte Carlo simulation da ta obtained by us and reasonable agreement is found. Also the location of the freezing transition is compared with available estimates based on extensive simulations performed by other groups. Although our mean -field-type theory does not take proper account of fluctuations and de fects (which are believed to be important to determine the nature of t his transition) are not treated at all, its prediction for the transit ion densities are quantitatively correct: however, the density gap at the (first-order) transition is overestimated. In addition, we observe that our results for the location of the transition crucially depend on how accurately the weighting function models the direct correlation function of the uniform fluid: As this description becomes better, th e agreement with simulations improves.