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.

• Received 23 October 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.4014