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We present a simple mean-field theory to study the effects of an external magnetic field on biaxial nematic liquid crystals. Isotropic-uniaxial nematic-biaxial nematic phase sequence in an external magnetic field is described. We determine the temperature-field phase diagrams. The model predicts two new phase diagrams. It is shown that in the presence of the magnetic field, the first order uniaxial nematic to biaxial nematic and isotropic to uniaxial nematic phase transitions become second order transition at a tricritical point.

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