Universal mean-field phase diagram for biaxial nematics

Fully attractive and partly repulsive molecular interactions,
characteristic of biaxial liquid crystal molecules,
are described by a class of quadratic Hamiltonians,
originally put forward by Straley.
The partly repulsive interactions require a minimax principle for
the associated mean-field free energy.
By analyzing the different phases in a bifurcation scenario,
we show that the phase diagram described by Sonnet et al. [Phys. Rev. E 67
061701 (2003)] is universal.
Our model predictions are in agreement
with recent observations on both V-shaped and tetrapodal
molecules.