Abstract
A nonlinear differential equation for the pressure P of a hard-core system gives rise to a unique solution for P< P 0 and a separate unique solution for P> P 0. The former corresponds to the uniform liquid and the latter to the crystalline solid. The two distinct solutions of the differential equation are separated by the singular solution P = P 0 which represents the liquid-solid coexistence phase. The existence of a singular solution signals the translational symmetry breaking associated with the liquid-solid transition. The hard-disk and hard-sphere freezing and melting transition densities obtained compare well with computer simulation results.
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