Numerical experiment on two-dimensional electron liquids. Thermodynamic properties and onset of short-range order

Thermodynamic properties of two-dimensional electron liquids are determined by numerical experiments over the domain of the plasma parameter $\epsilon =\frac{2\pi n{e}^4}{T^2}$, $0.05\le \epsilon \le 5\times {10}^3$, where $n$, $e$, and $T$ denote the number density, the unit charge, and the temperature in energy units, respectively. The correlation energy thus obtained is consistent with both the result of the plasma-parameter expansion calculation and that of earlier numerical experiments in the high-density domain. The pair correlation function $g\left(r\right)\mathrm{}$ agrees with the analytical result when $\epsilon$ is small. Short-range order appears at the critical plasma parameter ${\epsilon }_{\mathrm{sr}}$ in the range $10<\mathrm{}{\epsilon }_{\mathrm{sr}}<15\mathrm{}$. It is pointed out that the two-dimensional screening function $h\left(r\right)=\ln \mathrm{}\left[g\right(r)+1]+\frac{e^2}{\mathrm{Tr}}$ is approximately a linear function of the radius $r$ in the short-range domain, as in the case of three dimensions.