  We study the combined effect of cubic anisotropy and quenched uncorrelated
impurities on multicomponent spin models. For this purpose, we consider the
field-theoretical approach based on the Ginzburg-Landau-Wilson $\phi^4$
Hamiltonian with cubic-symmetric quartic interactions and quenched randomness
coupled to the local energy density. We compute the renormalization-group
functions to six loops in the fixed-dimension (d=3) perturbative scheme. The
analysis of such high-order series provides an accurate description of the
renormalization-group flow. The results are also used to determine the critical
behavior of three-dimensional antiferromagnetic three- and four-state Potts
models in the presence of quenched impurities.
