  We study the fate of double-Weyl fermions in three-dimensional systems in the
presence of long-range Coulomb interactions. By employing the momentum-shell
renormalization group approach, we find that the fixed point of noninteracting
double-Weyl fermions is unstable against Coulomb interactions and flows to a
nontrivial stable fixed point with anisotropic screening effect. Moreover,
experimentally measurable quantities such as specific heat obtain unusual
logarithmic corrections. We also discuss implications of our results to
three-dimensional materials HgCr2Se4 and SrSi2, candidate materials of hosting
double-Weyl fermions.
