  The spin transitions in the fractional quantum Hall effect provide a direct
measure of the tiny energy differences between differently spin-polarized
states, and thereby serve as an extremely sensitive test of the quantitative
accuracy of the theory of the fractional quantum Hall effect, and, in
particular, of the role of Landau-level mixing in lifting the particle-hole
symmetry. We report on an accurate quantitative study of this physics,
evaluating the effect of Landau-level mixing in a nonperturbative manner using
a fixed-phase diffusion Monte Carlo method. We find excellent agreement between
our calculated critical Zeeman energies and the experimentally measured values.
In particular, we find, as also do experiments, that the critical Zeeman
energies for fractional quantum Hall states at filling factors $\nu=2-n/(2n\pm
1)$ are significantly higher than those for $\nu=n/(2n\pm 1)$, a quantitative
signature of the lifting of particle-hole symmetry due to Landau-level mixing.
