Glassy liquid crystalline systems are expected to show significant history-dependent effects. Two model glassy systems are the RAN and SSS lattice models. The RAN model is a Lebwohl-Lasher lattice model with locally coupled nematic spins, together with uncorrelated random anisotropy fields at each site, while the SSS model has a finite concentration of impurity spins frozen in random directions. Here Brownian simulation is used to study the effect of different sample histories in the low temperature regime in a three dimensional (d = 3) model intermediate between SSS and RAN, in which a finite concentration p < pc (pc the percolation threshold) of frozen spins interacts with neighboring nematic spins with coupling W . Simulations were performed at temperature T ∼ TNI /2 (TNI the bulk nematic-isotropic transition temperature) for temperature-quenched and field-quenched histories (TQH and FQH respectively), as well as for temperature-annealed histories (AH). The first two of these limits represent extreme histories encountered in typical experimental studies. Using long-time averages for equilibrated systems, we calculate orientational order parameters and two-point correlation functions. Finite size-scaling was used to determine the range of the orientational ordering, as a function of coupling strength W, p and sample history. Sample history plays a significant role; for given concentration p, as disorder strength W is increased, TQH systems sustain quasi-long-range (QLRO) and short-range-order (SRO). The data are also consistent with a long-range order (LRO) phase at very low disorder strength. By contrast, for FQH, only LRO and QLRO occur within the range of parameters investigated. The crossover between regimes depends on history, but in general, the FQH phase is more ordered than than the AH phase, which is more ordered than the TQH phase. We detect also in the QLRO phase a domain-type structural pattern, consistent with ideas introduced by Giamarchi and Doussal [Phys. Rev. B 52, 1242Rev. B 52, (1995] on superconducting flux lattices. In phases in which short-range exponential order occurs, the orientational correlation length in the weak-disorder limit obeys Larkin-Imry-Ma scaling ξ ∼ D −2/(4−d) .

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Within the Landau-de Gennes phenomenological theory, we study the influence of an applied electric field with average strength E{a} on the position of a nematic line defect with topological charge M=+/-1/2 in a hybrid cell. We explore the biaxial structure of the defect core and we describe its expulsion from the cell upon increasing E{a}. We show that prior to the expulsion the defect core displays dramatic changes for strong enough surface anchorings. At a critical value of E{a}, the core broadens and merges into a surface layer with a large biaxiality. This transition corresponds to the reconstruction of the nematic order already observed in the bulk in response to an applied electric field. A similar order reconstruction could take place even in the absence of defects, but at a higher threshold.

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.

Universal behavior related to continuous symmetry breaking in nematic liquid crystals is studied using Brownian molecular dynamics. A three-dimensional lattice system of rod-like objects interacting via the Lebwohl-Lasher interaction is considered. We test the applicability of predictions originally derived in cosmology and magnetism. In the first part we focus on coarsening dynamics following the temperature driven isotropic-nematic phase transition for different quench rates. The behavior in the early coarsening regime supports predictions made originally by Kibble in cosmology. For fast enough quenches, symmetry breaking and causality give rise to a dense tangle of defects. When the degree of orientational ordering is large enough, well defined protodomains characterized by a single average domain length are formed. With time subcritical domains gradually vanish and supercritical domains grow with time, exhibiting a universal scaling law. In the second part of the paper we study the impact of random-field-type disorder on a range of ordering in the (symmetry broken) nematic phase. We demonstrate that short-range order is observed even for a minute concentration of impurities, giving rise to disorder in line with the Imry-Ma theorem prediction only for the appropriate history of systems.

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We report a theoretical study of various structures of chiral nematic liquid crystals, confined to submicrometer cylindrical cavities with tangential anchoring conditions. The Frank-Oseen free energy with additional surface energy terms is used to find nematic director fields, free energies, and stability diagrams of relevant structures. The dependence of various chiral nematic structures on the chirality parameter, pore size, elastic constants, and polar and azimuthal surface anchoring strengths is studied. We are particularly interested in the influence of the saddle-splay elastic constant on the structures. For ordinary values of material parameters, only radially twisted and asymmetric conical structure are stable. The former is stable at low chiralities, while the latter is stable for high chiralities. The radially twisted structure is commonly known as double twisted structure, while the asymmetric conical structure has not been considered, to the authors' knowledge. The phase diagram including both structures is determined by comparing their free energies. Theoretical predictions are in agreement with available experimental data. ͓S1063-651X͑96͒01811-9͔