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 ξ for random and homogeneous initial configurations. We determine the crossover fields B(c)(p) separating roughly the ordered and disordered regime. Memory effects are apparent only in the latter case, i.e. for B < B(c).PACS numbers: 47.51.+a, 47.54.-r, 07.05.Tp, 61.30.-v.
Keywords: Imry-Ma theorem; disorder; liquid crystals; memory effect; orientational order.