Does the isotropic–biaxial nematic transition always exist? A new topology for the biaxial nematic phase diagram

The biaxial nematic phase diagram for the second rank Straley quadrupolar pair potential, as explored until now, implies that a direct transition from a biaxial nematic to an isotropic phase can occur, either at a single Landau point or even, as recently shown using mean field theory, along a line. We show by an extensive Monte Carlo investigation that a different topology can be found in a wide region of parameter space, with the passage from biaxial to isotropic always going through a uniaxial phase. We argue that this may hint in part at the difficulty in realising a biaxial nematic phase.