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 $\mathrm{}(d=3\mathrm{})\mathrm{}$ 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.

• Received 25 February 2002

DOI:https://doi.org/10.1103/PhysRevB.67.024418