Equilibrium Pair-Correlation Function for a Two-Dimensional Plasma

The pair-correlation function for a one-component, two-dimensional classical plasma is investigated within the framework of the Debye approximation along the lines of the Cohen-Murphy method through a potential of average force, $w_2\left(\mathcal{r}\right)$, up to third order in the plasma parameter $\frac{q^2}{k_{\mathrm{B}}T}$. The $w_2\left(\mathcal{r}\right)$ short-range behavior appears to be an easily renormalizable quantity, while the long-range behavior confirms previous three-dimensional results.