A modified epsilon expansion for a Hamiltonian with cubic point-group symmetry

Abstract

The critical behaviour, in zero field above the critical temperature, of a hamiltonian with hypercubic point-group symmetry is studied in the framework of the epsilon expansion. An exponent associated with the anisotropy parameter Delta is calculated to order epsilon ³. It does not determine reliably whether or not Delta is an irrelevant variable in the critical region in three dimensions. The general structure of correlation functions is examined and found to be more complicated than in the isotropic case. It is suggested that these additional complications may be at least partially simplified by modifying the eigenvalue condition on the isotropic coupling constant to include the anisotropic coupling Delta .