Global equation of state of two-dimensional hard sphere systems

Hard sphere systems in two dimensions are examined for arbitrary density. Simulation results are compared to the theoretical predictions for both the low- and the high-density limit, where the system is either disordered or ordered, respectively. The pressure in the system increases with the density, except for an intermediate range of volume fractions 0.65<~ν<~0.75, where a disorder-order phase transition occurs. The proposed global equation of state (which describes the pressure for all densities) is applied to the situation of an extremely dense hard sphere gas in a gravitational field and shows reasonable agreement with both experimental and numerical data.