  Influence of an external magnetic field on the nematic-isotropic ($N-I$)
phase transition in a dispersion model of nematic liquid crystals, where the
molecules are either perfectly uniaxial or biaxial (board-like), has been
studied by Monte Carlo simulation. Using multiple histogram reweighting
technique and finite size scaling analysis the order of the phase transition,
the transition temperature at the thermodynamic limit and the stability limit
of the isotropic phase below the transition temperature for different magnetic
field strengths have been determined. The magnetic field dependence of the
shift in $N-I$ transition temperature is observed to be more rapid than that
predicted 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 transition
temperature is higher for the biaxial molecules in comparison with the uniaxial
case. The study shows that the $N-I$ transition for the biaxial molecules is
weaker than the well known weak first order $N-I$ transition for the uniaxial
molecules and the presence of the external magnetic field (up to a certain
critical value) makes the transition much more weaker for both the systems. The
estimate of the critical magnetic field ($\sim 110 T$) for the common nematics
is found to be smaller than the earlier estimates.
