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We investigate the spin-dependent effective electron-electron
interactions in a uniform system of two-dimensional electrons to
understand the spontaneous magnetization expected to occur at very
low density. For this purpose, we adopt the Kukkonen-Overhauser
form for the effective interactions which are built by accurately
determined local-field factors describing the charge and spin
fluctuations. The critical behavior of the effective interaction
for parallel spin electrons allows us to quantitatively locate the
transition to the ferromagnetic state at $r_{s}\approx27$. When
the finite width effects are approximately taken into account the
transition occurs at $r_{s}\approx30$ in agreement with recent
quantum Monte Carlo calculations.
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