Search for multiple-step integer quantum Hall transitions

Recent experiments in the integer quantum Hall regime seem to find direct transitions from quantum Hall states with Hall conductance ${\ensuremath{\sigma}}_{\mathrm{xy}}{=ne}^{2}/h$ with integer $n>1,$ to an insulating state in weak magnetic fields. We study the issue of quantum Hall transitions with change in Hall conductance ${\mathrm{ne}}^{2}/h$ with $n>1$ using a variation of the tight-binding lattice model for noninteracting electrons. Although such transitions do exist in our model for special tuning of parameters, they generically split, with the Hall conductance changing by ${e}^{2}/h$ at each transition. This suggests that a generic multiple step quantum Hall transition is incompatible with a noninteracting electron picture.