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The tri-critical point in the Blume-Emery-Griffiths model

The tri-critical behaviour of the spin-one Blume-Emery-Griffiths Ising model is investigated by means of the recently developed effective-field theory based on an extension of the Honmura-Kaneyoshi technique. The dependence of the position of the tri-critical point on the relative strengths of the bi-quadratic and bi-linear exchange interactions is investigated for the honeycomb, square and cubic lattices.