The Helmholtz free energy $F$ of the 2D electron fluid is calculated using a mapping to a classical Coulomb fluid [Phys. Rev. Lett. 87, 206404 (2001)]. For density parameters $r_s$ such that $\sim 25>r_s$, the fluid is unpolarized at all temperatures $t=T/E_F$, where $E_F$ is the Fermi energy. For higher $r_s$, the system is fully spin polarized for $t$ smaller than $\sim 0.35$, and partially polarized for $\sim 0.35<t<2$, depending on the density. At $r_s\sim 25–30$, and $t\sim 0.35$, an “ambispin” phase where $F$ is almost independent of the spin polarization is found. These results support claims for a stable, fully polarized fluid phase at $T=0$ for $r_s$ larger than $\sim 25–26$ and establish them for finite $T$ as well.

• Received 1 October 2002

DOI:https://doi.org/10.1103/PhysRevLett.90.136601