epsilon -expansion analysis of some physically realizable n⩾4 vector models

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Abstract
Four different n>or=4 component Hamiltonians describing phase transitions in certain physical systems are derived. The corresponding critical behaviour is studied using the exact renormalization group in d=4- epsilon dimensions. In particular, although TbD2, Nd and K2IrCl6 have different symmetries, their critical behaviour is described by the same anisotropic n=6 Hamiltonian and is predicted to correspond to the same fixed point. For three Hamiltonians, no stable fixed point exists.