Critical behaviour and cubic anisotropy

Abstract

The influence of the cubic anisotropy both in the quadratic and quartic part of an n-component 'spin' Hamiltonian is examined in the framework of a parquet-graph summation. For values of the anisotropy parameter f larger than a critical value, f-, a first-order transition occurs which corresponds to the appearance of complex fixed points in the renormalization group approach. On the other hand for f<f- a first- or second-order transition occurs depending on f, n and the values of the bare coupling constants. For second-order transitions a quantity m(n,f) plays the role of an effective number of components, m(n,0)=n. For m>4 and m<-8 the system has a strongly cubic behaviour whereas 0<m<4 a weakly cubic behaviour is observed; the latter changes to pure isotropic behaviour for f to 0. For -8<m<0 the behaviour is strongly or weakly cubic depending on the values of the bare coupling constants.