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The random-magnetic-field classical Heisenberg model is solved in spatialdimensions d>=2 using the recently developed Fourier-Legendrerenormalization-group theory for $4\pi$ steradians continuously orientablespins, with renormalization-group flows of 12,500 variables. Therandom-magnetic-field Heisenberg model is exactly solved in 10 hierarchicalmodels, for d=2,2.26,2.46,2.58,2.63,2.77,2.89,3. For non-zero random fields,ferromagnetic order is seen for d>2. This ordering shows, at d=3, reentrance asa function of temperature.

Reentrant Ferromagnetic Ordering of the Random-Field Heisenberg Model in d>2 Dimensions: Fourier-Legendre Renormalization-Group Theory