Reentrant ferromagnetic ordering of the random-field Heisenberg model in d>2 dimensions: Fourier-Legendre renormalization-group theory.

The random-magnetic-field classical Heisenberg model is solved in spatial dimensions d≥2 using the recently developed Fourier-Legendre renormalization-group theory for 4π steradians continuously orientable spins, with renormalization-group flows of 12 500 variables. The random-magnetic-field Heisenberg model is exactly solved in 10 hierarchical models, for d=2,2.26,2.46,2.58,2.63,2.77,2.89,3. For nonzero random fields, ferromagnetic order is seen for d>2. This ordering, at d=2.46,2.58,2.63,2.77,2.89,3, shows reentrance as a function of temperature.