We study classical Heisenberg antiferromagnets with uniaxial exchange anisotropy and a cubic anisotropy term on simple cubic lattices in an external magnetic field using ground state considerations and extensive Monte Carlo simulations. In addition to the antiferromagnetic phase field--induced spin--flop and non--collinear, biconical phases may occur. Phase diagrams and critical as well as multicritical phenomena are discussed. Results are compared to previous findings.
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