We studied pattern characteristics in randomly perturbed structures exhibiting continuous symmetry breaking. A Lebwohl-Lasher-type lattice model was used which described well the onset of orientational ordering of a system of rod-like objects. For example, such systems mimic the orientational ordering tendency in liquid crystals or in an ensemble of nanotubes. We set impurities to impose a random anisotropy type of disorder on the objects. Structural characteristics were studied as a function of concentration of impurities, interaction strength w between impurities and rod-like objects, external ordering strength and history of samples. We showed that the characteristic linear size of patterns and range of ordering strongly depend on the history of samples for weak enough strength w. The two-dimensional and three-dimensional simulations yielded qualitatively similar results.

SummaryOrientational ordering of a homogeneous mixture of uniaxial liquid crystalline (LC) molecules and magnetic nanoparticles (NPs) is studied using the Lebwohl–Lasher lattice model. We consider cases where NPs tend to be oriented perpendicularly to LC molecules due to elastic forces. We study domain-type configurations of ensembles, which are quenched from the isotropic phase. We show that for large enough concentrations of NPs the long range uniaxial nematic ordering is replaced by short range order exhibiting strong biaxiality. This suggests that the impact of NPs on orientational ordering of LCs for appropriate concentrations of NPs is reminiscent to the influence of quenched random fields which locally enforce a biaxial ordering.

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