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The effective g factor (g(*)) of a dilute interacting two-dimensional electron system is expected to increase with respect to its bare value as the density is lowered, and to eventually diverge as the system makes a transition to a ferromagnetic state. We report here measurements of g(*) in dilute (density 0.8 to 6.5x10(10) cm(-2)), high-mobility GaAs two-dimensional electrons from their spin polarization in a parallel magnetic field. The data reveal a surprising trend. While g(*) is indeed significantly enhanced with respect to the band g factor of GaAs, the enhancement factor decreases from about 6 to 3 as the density is reduced.
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