N-component Ginzburg-Laudau Hamiltonian with cubic anisotropy: A six-loop study

We consider the Ginzburg-Landau Hamiltonian with a cubic-symmetric quartic interaction and compute the renormalization-group functions to six-loop ord er in d=3. We analyze the stability of the fixed points using a Borel trans formation and a conformal mapping that takes into account the singularities of the Borel transform. We find that the cubic fixed point is stable for N >N-c, N-c=2.89(4). Therefore, the critical properties of cubic ferromagnets are not described by the Heisenberg isotropic Hamiltonian, but instead by the cubic model at the cubic fixed point. For N=3, the critical exponents a t the cubic and symmetric fixed points differ very little (less than the pr ecision of our results, which is less than or similar to 1% in the case of gamma and nu). Moreover? the irrelevant interaction bringing from the symme tric to the cubic fixed point gives rise to slowly decaying scaling correct ions with exponent omega(2)=0.010(4). For N=2, the isotropic fixed point is stable and the cubic interaction induces scaling corrections with exponent omega(2)=0.103(8). These conclusions are confirmed by a similar analysis o f the five-loop epsilon expansion. A constrained analysis, which takes into account that N-c=2 in two dimensions, gives N-c=2.87(5).