Effects of electron-electron interactions on the integer quantum Hall transitions.
We study the effects of the electron-electron interaction on the critical properties of the plateau transitions in the integer quantum Hall effect. We find the renormalization group dimension associated with short-range interactions to be $\ensuremath{-}0.66\ifmmode\pm\else\textpm\fi{}0.04$. Thus the noninteracting fixed point (characterized $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ and $\ensuremath{\nu}\ensuremath{\approx}2.3$) is stable. For the Coulomb interaction, we find the correlation effect is a marginal perturbation at a Hartree-Fock fixed point ( $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, $\ensuremath{\nu}\ensuremath{\approx}2.3$) by dimension counting. Further calculations are needed to determine its stability upon loop corrections.