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 (formula presented) with integer (formula presented) to an insulating state in weak magnetic fields. We study the issue of quantum Hall transitions with change in Hall conductance (formula presented) with (formula presented) 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 (formula presented) at each transition. This suggests that a generic multiple step quantum Hall transition is incompatible with a noninteracting electron picture.