Spin-Singlet to Spin Polarized Phase Transition at $\nu=2/3$: Flux-Trading in Action

We analyze the phase transition between spin-singlet and spin-polarized states which occurs at $\nu=2/3$. The basic strategy is to use adiabatic flux-trading arguments to relate this transition to the analogous transition at $\nu=2$. The transition is found to be similar to a transition in ferromagnets. In our analysis, we find two possible scenarios. In one, the transition is first-order, in agreement with experimental and numerical studies of the $\nu=2/3$ transition. In the other, we find a second-order transition to a partially polarized state followed by a second-order transition to a fully polarized state. This picture is in qualitative agreement with experiments on the $\nu=4/3$ state, the particle-hole conjugate of $\nu=2/3$. We analyze the edge modes which propagate at the boundaries between regions of different phases and show that these do not support gapless excitations. Finally, we consider the possibility of a finite-temperature compressible state with a Fermi surface which would explain the non-zero $\rho_{xx}$ seen in experiments.