Phase diagram of the two-dimensional electron liquid

The phase diagram of a two-dimensional electron liquid immersed in a uniform background of charge is analyzed. We present a qualitative argument based on energy considerations alone which yields the shape of the liquid-solid boundary. To determine absolute values of the density and temperature we utilize a microscopoic theory based on the self-consistent harmonic approximation to the phonon spectrum of a solid. This theory is a one-phase instability theory of the long-wavelength transverse mode in the solid phase alone. It yields values of $r_s\approx 5$ in the quantum regime and ${\Gamma }_0=3\mathrm{}$ in the classical case.