Competition between local disordering and global ordering fields in nematic liquid crystals

We study the influence of external electric or magnetic field B on orientational ordering of nematic liquid crystals or of other rod-like objects (e.g. nanotubes immersed in a liquid) in the presence of random anisotropy field type of disorder. The Lebwohl-Lasher lattice type of semi-microscopic approach is used at zero temperature. Therefore, results are valid well below the transition into the isotropic phase. We calculate the correlation function of systems as a function of B, concentration p of impurities imposing random anisotropy field disorder, the disorder strength W and system dimensionality (2D and 3D systems). In order to probe memory effects we calculate correlation length ▫$xi$▫ for random and homogeneous initial configurations. We determine the crossover fields Bc(p) separating roughly the ordered and disordered regime. Memory effects are apparent only in the latter case, i.e. for B < Bc