Lebwohl-Lasher model

Zhang Z, Mouritsen O G and Zuckermann M J 1992 Weak first-order orientational transition in the Lebwohl-Lasher model of liquid crystals Phys. Rev.L 69 2803-6... 

Zhang Z, Zuckermann M J and Mouritsen O G 1993 Phase transition and director fluctuations in the 3-dimensional Lebwohl-Lasher model of liquid crystals/Mo/. Phys. 80 1195-221... 

To calculate morphologies of phase separation of PDLCs, many simulation methods have been developed [137]. Zhu et al. [138] have performed a Monte Carlo simulation to investigate the phase behaviors of PDLC by using the Lebwohl-Lasher model for nematogens [139]. One of the methods is to numerically solve the... 

Fabbri U and Zannoni C 1986 A Monte Carlo investigation of the Lebwohl-Lasher lattice model in the vicinity of its orientational phase transition Mol. Phys. 58 763-88... 

Abstract The influence of randomly distributed impurities on liquid crystal (LC) orientational ordering is studied using a simple Lebwohl-Lasher t5q)e lattice model in two d=2) and three d=3) dimensions. The impurities of concentration p impose a random anisotropy field-type of disorder of strength w to the LC nematic phase. Orientational correlations can be well presented by a single coherence length for a weak enough w. We show that the Imry-Ma... 

Our simulations use a lattiee-spin model of a liquid erystal, of the t5q)e pioneered by Lebwohl and Lasher. We use a simple Lebwohl-Lasher pairwise interaetion among rod-like lattiee spins S,. The nature of the energy means that, as with all liquid erystal systems, there is never a distinction between S and - S. This ean simulate either a thermotropie or a lyotropic LC. The sites are arranged in a ri-dimensional eubie lattiee, of length L lattice constants, with total number of sites (i.e. partieles) N = lf, subjeet to periodic boundary conditions. In all subsequent work, distanees are scaled with respect to the lattiee eonstant. 

In the quest for a universal feature in the short-to-intermediate time orientational dynamics of thermotropic liquid crystals across the I-N transition, Chakrabarti et al. [115] investigated a model discotic system as well as a lattice system. As a representative discotic system, a system of oblate ellipsoids of revolution was chosen. These ellipsoids interact with each other via a modified form of the GB pair potential, GBDII, which was suggested for disc-like molecules by Bates and Luckhurst [116]. The parameterization, which was employed for the model discotic system, was k = 0.345, Kf = 0.2, /jl= 1, and v = 2. For the lattice system, the well-known Lebwohl-Lasher (LL) model was chosen [117]. In this model, the particles are assumed to have uniaxial symmetry and represented by three-dimensional spins, located at the sites of a simple cubic lattice, interacting through a pair potential of the form... 

Figure 13. Orientational dynamics of the Lebwohl-Lasher lattice model (N = 1000) at temperatures near the isotropic-nematic transition, (a) Time evolution of the single-particle second-rank orientational time correlation function in a log-log plot at temperatures T = 1.213,1.176, 1.160,1.149,1.134. Temperature decreases from left to right, (b) Decay of the OKE signal in a log-log plot at short-to-intermediate time window at temperatures T = 1.176, and 1.149. Temperature decreases from top to bottom on the left side of the plot. The dashed lines are the simulation data and the continuous lines are the linear fits to the data. The system undergoes a transition from the isotropic to the nematic phase at T 1.14. (Reproduced from Ref. 115.)...

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