Recent experiments report that the long looked for thermotropic biaxial
nematic phase has been finally detected in some thermotropic liquid crystalline
systems. Inspired by these experimental observations we concentrate on some
elementary theoretical issues concerned with the classical sixth-order
Landau-deGennes free energy expansion in terms of the symmetric and traceless
tensor order parameter Qαβ. In particular, we fully explore the
stability of the biaxial nematic phase giving analytical solutions for all
distinct classes of the phase diagrams that theory allows. This includes
diagrams with triple- and (tri-)critical points and with multiple (reentrant)
biaxial- and uniaxial phase transitions. A brief comparison with predictions of
existing molecular theories is also given.Comment: 12 pages, 14 figure
