Exact two-dimensional plasma pair-correlation function in the Singwi-Tosi-Land-Sjolander approximation. I.k-space solutions and thermodynamic properties

The Singwi-Tosi-Land-Sjolander (STLS) nonlinear integral equation for the plasma pair-correlation function $g$ is adapted to two-dimensional one-component plasma (ocp) systems whose Coulombic interactions are characterized by the logarthmic potential. The two-dimensional STLS integral equation has the remarkable property that it can be exactly solved. The resulting expressions for $g\left(k\right)\mathrm{}$ are extensively analyzed and are shown to be negative definite for all values of $k$ and the coupling strength. The implication here is that in the STLS approximation, the ocp liquid can never undergo a phase transition. Exact expressions for $g$ enable us to evolve exact formulas for the correlation energy and heat capacity. Finally, we demonstrate that the STLS approximation scheme exactly reproduces the correct equation of state for the two-dimensional ocp liquid.