Critical behaviour of anisotropic cubic systems

The critical behavior of an anisotropic classical Heisenberg ferromagnet with cubic point-group symmetry is studied in the limit where the spin-dimensionality N is large. The system is shown to undergo a first order phase transition. Corrections of order 1/N are calculated for a critical exponent describing the behaviour of the transverse susceptibility in zero magnetic field below the critical temperature. For small anisotropy and to order 1/N the equation of state is identical to the isotropic calculation when expressed in terms of longitudinal and transverse susceptibilities, temperature and magnetization, except for a shift in the critical temperature.