Universal mean-field phase diagram for biaxial nematics obtained from a minimax principle

We study a class of quadratic Hamiltonians which describe both fully attractive and partly repulsive molecular
interactions, characteristic of biaxial liquid crystal molecules. To treat the partly repulsive interactions
we establish a minimax principle for the associated mean-field free energy. We show that the phase diagram
described by Sonnet et al. [Phys. Rev. E 67, 061701 (2003)] is universal. Our predictions are in good
agreement with the recent observations on both V-shaped and tetrapodal molecules.