Statistical physics of the two-dimensional Coulomb liquid with ionic hard-core size

A self-consistent theory of bulk electrolytes incorporating electrostatic and hard-core interactions on an equal level is applied to the two-dimensional Coulomb liquid with finite ion size. The ionic pair distributions, the structure factors, and the thermodynamic functions of the formalism are compared with extensive Monte Carlo simulation results from the literature. At moderate salt densities, our computational approach can accurately describe the thermodynamics of two-dimensional solutions across weak to intermediate coupling strengths. The improved accuracy of the present theory with respect to continuum approaches stems mainly from its ability to account for the non-uniform screening of electrostatic interactions associated with the impenetrability of the charged hard disks by their ionic atmosphere. Due to the underestimation of the ionic clusters emerging in the dilute regime, the validity domain of our self-consistent formalism shrinks with the decrease of the salt density. As a result, our approach cannot reach the critical coupling domain where the conductor-insulator transition of two-dimensional charged hard disks occurs. This indicates that approaching the low-temperature dielectric phase via the present formalism will require extending the underlying self-consistent approximation at least to the next cumulant order.