# Cooperative magnetism in metallic jellium and in the insulating Wigner electron crystal

## Abstract

Total energies for the paramagnetic (P) and ferromagnetic (F) metallic phases of jellium are calculated using interpolation formulae adjusted to the results of computer simulation studies. For the Wigner insulator (W), the total energy given by an early theoretical model is found to agree closely with recent computer simulation results. Using these total energies, the phase transitions from P to F and from F to W are estimated to take place at rs = 79 ± and 84 ± 4, respectively, in units of the Bohr radius. Although consistent with earlier estimates based directly on the computer simulations at a limited number of rs values, the present estimates are more precise. Since the P to F and F to W transitions come so close together on an rs scale, the F phase may just barely emerge as the lowest energy phase or may not so emerge at all. Using the virial theorem, kinetic energy curves are constructed and kinetic energy discontinuities at the first-order phase transitions are thereby estimated. The momentum distributions for various phases of jellium are also discussed in terms of simple models. Finally, the phase boundary between antiferromagnetic and paramagnetic states of the Wigner crystal for T ≠ 0 is briefly considered. It is shown that one is dealing with antiferromagnetism in the millidegree Kelvin range. © 1984.