Exact renormalization group recursion formulas, derived in Paper I for ε=4-d small, are applied to antiferromagnets. It is shown, that in contrast to the ferromagnetic case, the main parameters characterizing the dipolar interactions become irrelevant for antiferromagnets, so that the critical exponents maintain their short-range values. However, the relative decay of the dipolar parameters is slow (the appropriate exponents being of order ε2), and thus the possibility of observing their existence experimentally is discussed briefly. In addition, the dipolar anisotropies, deriving from the lattice structure, produce weak instabilities which are even harder to detect than in the ferromagnetic case. Ferromagnetic short-range anisotropy is considered briefly. The Appendix contains a calculation of the renormalization group eigenvalues of the operators SR→4 and (SR→a)4. The latter is shown to be relevant.