We analyze the global phase diagram of a Maier-Saupe lattice model with theinclusion of disorder degrees of freedom to mimic a mixture of oblate andprolate molecules (discs and cylinders). In the neighborhood of a Landaumulticritical point, solutions of the statistical problem can be written as aLandau-de Gennes expansion for the free energy. If the disorder degrees offreedom 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 atwo-temperature formalism to mimic the presence of two distinct relaxationtimes, and show that a slight departure from complete thermalization is enoughto stabilize a biaxial nematic phase.
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