Luckhurst-Romano model of thermotropic biaxial nematic phase

Recent experiments show that the long looked for thermotropic biaxial nematic phase is finally stabilized in a low mass liquid crystalline system. Inspired by this experimental observation we concentrate on some theoretical issues concerned with this phase. In particular we show that the simplest Lebwohl-Lasher biaxial model, as introduced by Luckhurst and Romano, is consistent with the minimal coupling Landau-de Gennes phenomenological approach. The model shows a rich spectrum of possibilities, in particular a direct isotropic-biaxial nematic phase transition. A possible bridge between molecular and phenomenological approaches, in particular an interpretation of the alignment tensor, is discussed.