We use the classical mapping of quantum fluids [Phys. Rev. Lett. 84, 959 (2000)] for a study of the uniform 2D electron gas. The “quantum temperature” $T_q$ of the classical 2D Coulomb fluid having the same correlation energy $E_c$ as the quantum fluid is determined as a function of the density parameter $r_s$. Using this $T_q$, spin-dependent pair-distribution functions are determined, and an analytic fit to the $E_c$ is given. The $T_q$ for 2D and 3D electron fluids is found to be approximately the same universal function of the classical coupling constant $\Gamma$. The coupling $\Gamma$ increases more rapidly with density in 2D; hence, we present a scheme for including bridge terms in the 2D hypernetted-chain method. The Helmholtz free energies of the spin-polarized and unpolarized phases are calculated, and the existence of a ferromagnetic phase near $r_s\sim 30$ is found to be a marginal possibility.

• Received 12 March 2001

DOI:https://doi.org/10.1103/PhysRevLett.87.206404