Zero Temperature Phases of the Electron Gas

TL;DR

This paper investigates the zero-temperature phases of the three-dimensional electron gas, revealing phase transitions from paramagnetic to ferromagnetic states and the formation of a ferromagnetic Wigner crystal at high densities.

Contribution

It provides a detailed analysis of phase transitions and stability ranges in the electron gas using stochastic methods, including the identification of a partially spin-polarized liquid phase.

Findings

Continuous transition from paramagnetic to ferromagnetic fluid

Intermediate stability range for partially spin-polarized liquid

Wigner crystal formation at high density (r_s=65 ± 10)

Abstract

The stability of different phases of the three-dimensional non-relativistic electron gas is analyzed using stochastic methods. With decreasing density, we observe a {\it continuous} transition from the paramagnetic to the ferromagnetic fluid, with an intermediate stability range ($25\pm 5 \leq r_s\leq 35 \pm 5$) for the {\it partially} spin-polarized liquid. The freezing transition into a ferromagnetic Wigner crystal occurs at $r_s=65 \pm 10$. We discuss the relative stability of different magnetic structures in the solid phase, as well as the possibility of disordered phases.