Critical Behavior of Anisotropic Cubic Systems in the Limit of Infinite Spin Dimensionality

Abstract

The zero-field critical behavior above ${T}_{c}$ of ferromagnets (or ferroelectrics) with a Hamiltonian of cubic symmetry is studied, in $d$ space dimensions, in the limit of infinite spin dimensionality, $n\ensuremath{\rightarrow}\ensuremath{\infty}$, with the cubic term of order unity, but the usual ${S}^{4}$ term of order ${n}^{\ensuremath{-}1}$. 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).