Solution of the Percus-Yevick equation for hard discs
M. Adda-Bedia, E. Katzav, D. Vella
TL;DR
This paper presents a numerical solution to the Percus-Yevick equation for hard disc fluids in two dimensions, providing accurate pair correlation functions and equations of state, with potential for generalization to higher even dimensions.
Contribution
The authors develop a simplified integral equation approach to solve the Percus-Yevick equation in 2D, achieving results consistent with Monte Carlo simulations and extendable to higher even dimensions.
Findings
Good agreement with Monte Carlo data
Accurate pair correlation functions obtained
Method applicable to higher even dimensions
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.
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