Solution of the Percus-Yevick equation for hard discs

Abstract

We solve the Percus-Yevick equation in two dimensions by reducing it to a set of simple integral equations. We numerically obtain both the pair correlation function and the equation of state for a hard disc fluid and find good agreement with available Monte-Carlo calculations. The present method of resolution may be generalized to any even dimension.

9 pages, 3 figures

References in corpus (4)

• Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions
• Structure of hard-hypersphere fluids in odd dimensions
• Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular dynamics simulations
• Percus-Yevick theory for the structural properties of the seven-dimensional hard-sphere fluid

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• Multicomponent fluids of hard hyperspheres in odd dimensions
• Diverging time scale in the dimensional crossover for liquids in strong confinement
• Random Close Packing and the Hard Sphere Percus-Yevick Theory
• Thermodynamics and structure of simple liquids in the hyperbolic plane
• Static properties of quasi-confined hard-sphere fluids
• Temperature Expansions in the Square-Shoulder Fluid I: the Wiener-Hopf Function
• Finite-size scaling functions of the phase transition in the ferromagnetic Ising model on random regular graphs
• Depletion force between disordered linear macromolecules