Ferromagnetism of the electron gas

The ground-state energy of the ferromagnetic electron gas is calculated for the relative polarizationζ=0−1 and the interelectron separationr _s =5−12. The method consists in describing the electron gas approximately by a quadratic boson Hamiltonian, and contains the random-phase approximation as a special case. Numerical studies show that in both the random-phase and the present approximations the paramagnetic state has the lowest energy: the energy increases withζ for all values ofr _s considered. In the present approximation instabilities are found to occur forr _s above a critical value, due to exchange processes of finite momentum transfers. Forζ=0 this critical value ofr _s is 9.4; it decreases with increasingζ. However, the fully-polarized state (ζ=1), which lies above the rest, is always stable. The conclusions are as follows: (1) Forr _s <9.4 the electron gas is paramagnetic. (2) Atr _s =9.4 it goes over to the fully-polarized ferromagnetic state. (3) This phase transition requires an energy absorption of 0.03 rydberg per electron. (4) The fully-polarized state is not obtainable as the limitζ→1.