  We analyze the global phase diagram of a Maier-Saupe lattice model with the
inclusion of disorder degrees of freedom to mimic a mixture of oblate and
prolate molecules (discs and cylinders). In the neighborhood of a Landau
multicritical point, solutions of the statistical problem can be written as a
Landau-de Gennes expansion for the free energy. If the disorder degrees of
freedom are quenched, we confirm the existence of a biaxial nematic strucure.
If orientational and disorder degrees of freedom are allowed to thermalize,
this biaxial solution becomes thermodynamically unstable. Also, we use a
two-temperature formalism to mimic the presence of two distinct relaxation
times, and show that a slight departure from complete thermalization is enough
to stabilize a biaxial nematic phase.
