Critical behavior of anisotropic cubic systems in the limit of infinite spin dimensionality

The zero-field critical behavior above Tc of ferromagnets (or ferroelectrics) with a Hamiltonian of cubic symmetry is studied, in d space dimensions, in the limit of infinite spin dimensionality, n, with the cubic term of order unity, but the usual S4 term of order n-1. A diagrammatic expansion about an Ising model (instead of the normal Gaussian model) is used. Characteristic cubic behavior is discovered, with renormalized Ising-model exponents (in the Fisher sense).