Correlations in two-dimensional electron systems. Magnetic properties

Abstract

The ground-state energies of (i) an ideal two-dimensional electron gas, (ii) a quasi-two-dimensional electron system resembling electrons trapped on a liquid-helium surface, (iii) a quasi-two-dimensional electron system resembling inversion layers of the Si(100)-Si${\mathrm{O}}_{2}$ system, and (iv) an ideal three-dimensional electron gas are obtained by numerically evaluating the sum of "ring diagram" contributions to the correlation energies for all magnetizations and a wide range of electron densities. The transition from nonmagnetic to ferromagnetic state is abrupt in (i) and (ii) and gradual in (iii) and (iv). It is argued that these transitions may occur in quasi-two-dimensional systems without violating the theorems on the nonexistence of long-range order in two dimensions because of the presence of weak long-range forces in such systems.