Coulomb interactions at quantum Hall critical points of systems in a periodic potential

We study the consequences of long-range Coulomb interactions at the critical points between integer/fractional quantum Hall states and an insulator. We use low energy theories for such transitions in anyon gases in the presence of an external periodic potential. We find that Coulomb interactions are marginally irrelevant for the integer quantum Hall case. For the fractional case, depending upon the anyon statistics parameter, we find behavior similar to the integer case, or flow to a novel line of fixed points with exponents $z=1$, $\nu > 1$ stable against weak disorder in the position of the critical point, or run-away flow to strong coupling.