The 2-D electron system (2DES) in Si metal-oxide field-effect transistors
(MOSFETS) consists of two distinct electron fluids interacting with each other.
We calculate the total energy as a function of the density n, and the spin
polarization ζ in the strongly-correlated low-density regime, using a
classical mapping to a hypernetted-chain (CHNC) equation inclusive of bridge
terms. Here the ten distribution functions, arising from spin and valley
indices, are self-consistently calculated to obtain the total free energy, the
chemical potential, the compressibility and the spin susceptibility. The T=0
results are compared with the 2-valley Quantum Monte Carlo (QMC) data of Conti
et al. (at T=0, ζ=0) and found to be in excellent agreement. However,
unlike in the one-valley 2DES, it is shown that {\it the unpolarized phase is
always the stable phase in the 2-valley system}, right up to Wigner
Crystallization at rs=42. This leads to the insensitivity of g∗ to the
spin polarization and to the density. The compressibility and the
spin-susceptibility enhancement calculated from the free energy confirm the
validity of a simple approach to the two-valley response based on coupled-mode
formation. The three methods, QMC, CHNC, and Coupled-mode theory agree closely.
Our results contain no {\it ad hoc} fit parameters. They agree with experiments
and do not invoke impurity effects or metal-insulator transition phenomenology.Comment: 10 pages 4 figure