Effect of a cubic crystal field on the critical behavior of a 3D model with Heisenberg exchange coupling: A high-temperature series investigation

The effect of a cubic anisotropy on the critical behavior of systems with isotropic exchange coupling has been the subject of many approximate renormalization-group studies with conflicting results for the n=3, Heisenberg case. These studies disagree on the relevance of cubic crystal-field strength, i.e., whether this field induces a crossover from the n=3 isotropic behavior to a distinctive cubic behavior or not. We have derived and analyzed tenth-order, high-temperature susceptibility series for the spin-infinity Heisenberg model with a nearest-neighbor exchange and a crystal field of cubic symmetry for the fcc lattice. The fixed length of the spins significantly affects the form of the series causing many terms to be zero. Analysis of our tenth-order series for fixed values of the cubic field strength ..nu../sub 4/ yields an effective susceptibility index which is indistinguishable from the Heisenberg value for ..nu../sub 4/< or approx. =5J, J being the exchange constant. Naive analysis of our series for the cubic field derivatives of the susceptibility suggests that the cubic field strength is a relevant variable with an associated crossover exponent phi=0.63 +- 0.10, much larger than the value, phiapprox.0.1, expected from the renormalization-group calculations.