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 $-0.66\mathrm{}\pm 0.04$. Thus the noninteracting fixed point (characterized $z=2\mathrm{}$ and $\nu \approx 2.3$) is stable. For the Coulomb interaction, we find the correlation effect is a marginal perturbation at a Hartree-Fock fixed point ( $z=1\mathrm{}$, $\nu \approx 2.3$) by dimension counting. Further calculations are needed to determine its stability upon loop corrections.