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The Helmholtz free energy F of the interacting 2-D electron fluid iscalculated nonperturbatively using a mapping of the quantum fluid to aclassical Coulomb fluid [Phys. Rev. Letters, vol. 87, 206404 (2001)]. Fordensity parameters rs such that rs<~25, the fluid is unpolarized at alltemperatures t=T/EF where EF is the Fermi energy. For lower densities, thesystem becomes fully spin polarized for t<~0.35, and partially polarized for0.35<t< 2, depending on the density. At rs ~25-30, and t ~0.35, an ''ambispin''phase where F is almost independent of the spin polarization is found. Theseresults support recent claims, based on quantum Monte Carlo results, for astable, fully spin-polarized fluid phase at T = 0 for rs larger than about25-26.

Spin-Polarized Stable Phases of the 2D Electron Fluid at Finite Temperatures