  We analyze the critical behavior of the dephasing rate induced by short-range
electron-electron interaction near an Anderson transition of metal-insulator or
quantum Hall type. The corresponding exponent characterizes the scaling of the
transition width with temperature. Assuming no spin degeneracy, the critical
behavior can be studied by performing the scaling analysis in the vicinity of
the non-interacting fixed point, since the latter is stable with respect to the
interaction. We combine an analytical treatment (that includes the
identification of operators responsible for dephasing in the formalism of the
non-linear sigma-model and the corresponding renormalization-group analysis in
$2+\epsilon$ dimensions) with numerical simulations on the Chalker-Coddington
network model of the quantum Hall transition. Finally, we discuss the current
understanding of the Coulomb interaction case and the available experimental
data.
