Modeling of Phase Transitions from Biaxial Nematic Liquid Crystals with Topological Defects

Abstract
In nematic liquid crystals (NLCs) topological defects of chiral nature play an essential role in phase transitions and lead to nontrivial topology. A number of "biaxial-uniaxial nematic" phase transitions are accompanied by a decrease in dimensionality, while the order parameter of the NLCs is connected with an evolution of topological defects, the surface anchoring energy and elastic Frank moduli. In this work the Landau-de Gennes theory for the biaxial nematics is presented as the chiral gauge field theory, which allows us to explain topologically dependent phase transitions. In this regard, we consider an example of numerical Monte Carlo modeling on a lattice describing the transformation of bulk disclinations in the biaxial nematic phase into the surface bojooms of a uniaxial NLC.

Keywords: biaxial nematics, topological defects, Monte Carlo lattice