Abstract
The ground state energies of (1) an ideal two-dimensional electron gas, (2) a quasi-two dimensional electron system resembling electrons trapped on a liquid helium surface, (3) a quasi-two dimensional electron system resembling inversion layers of Si(100)SiO 2 system, and (4) an ideal three-dimensional electron gas are obtained by numerically evaluating the sum of “ring diagrams” 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 (1) and (2) and gradual in (3) and (4).
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