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Influence of an external magnetic field on the nematic-isotropic ($N-I$)phase transition in a dispersion model of nematic liquid crystals, where themolecules are either perfectly uniaxial or biaxial (board-like), has beenstudied by Monte Carlo simulation. Using multiple histogram reweightingtechnique and finite size scaling analysis the order of the phase transition,the transition temperature at the thermodynamic limit and the stability limitof the isotropic phase below the transition temperature for different magneticfield strengths have been determined. The magnetic field dependence of theshift in $N-I$ transition temperature is observed to be more rapid than thatpredicted by the standard Landau-de Gennes and Maier-Saupe mean field theories.We have shown that for a given field strength the shift in the transitiontemperature is higher for the biaxial molecules in comparison with the uniaxialcase. The study shows that the $N-I$ transition for the biaxial molecules isweaker than the well known weak first order $N-I$ transition for the uniaxialmolecules and the presence of the external magnetic field (up to a certaincritical value) makes the transition much more weaker for both the systems. Theestimate of the critical magnetic field ($\sim 110 T$) for the common nematicsis found to be smaller than the earlier estimates.

Effect of an external magnetic field on the nematic-isotropic phase transition in mesogenic systems of uniaxial and biaxial molecules