We discuss the Lebwohl-Lasher model of nematic liquid crystals in a confined geometry, using Monte Carlo simulation and mean-field theory. A film of material is sandwiched between two planar, parallel plates that couple to the adjacent spins via a surface strength $ε_s$. We consider the cases where the favoured alignments at the two walls are the same (symmetric cell) or different (asymmetric or hybrid cell). In the latter case, we demonstrate the existence of a {\it single} phase transition in the slab for all values of the cell thickness. This transition has been observed before in the regime of narrow cells, where the two structures involved correspond to different arrangements of the nematic director. By studying wider cells, we show that the transition is in fact the usual isotropic-to-nematic (capillary) transition under confinement in the case of antagonistic surface forces. We show results for a wide range of values of film thickness, and discuss the phenomenology using a mean-field model.
The Lebwohl-Lasher model describes the isotropic-nematic transition in liquid crystals. In two dimensions, where its continuous symmetry cannot break spontaneously, it is investigated numerically since decades to verify, in particular, the conjecture of a topological transition leading to a nematic phase with quasi-long-range order. We use scale invariant scattering theory to exactly determine the renormalization group fixed points in the general case of $N$ director components ($RP^{N-1}$ model), which yields the Lebwohl-Lasher model for $N=3$. For $N>2$ we show the absence of quasi-long-rang…
High accuracy Monte Carlo study has been performed in the modified planar Lebwohl Lasher model containing and interaction, where and are second and fourth order Legendre polynomial having three-dimensional spin. Weakly First order Nematic to Isotropic phase transition is observed using this model. Extensive Monte Carlo simulations using Wolff algorithm are performed to investigate the average energy, order parameter, ordering susceptibility, entropy and specific heat near phase transition. Transition temperature is also estimated.
Wang-Landau Monte Carlo simulation of isotropic-nematic transition in liquid crystals
Wang和Landau最近提出了一种简单而灵活的非Boltzmann Monte Carlo方法来估计态密度，由此可以计算封闭系统的宏观性质。他们通过共连续能谱演示了他们的算法。本文对离散能谱的考虑系统进行了改进。我们发现，当系统具有连续的能量谱时，Wang-Landau算法不能很好地执行。在本文中，我们提出了修改的算法，并证明其性能的液晶系统的晶格模型（Lebwohl-Lasher相互作用具有连续变化的能量），表现出从高温各向同性到低温相变。
A system of optimal biaxial molecules placed at the sites of a cubic lattice is studied in an extended Lebwohl-Lasher model. Molecules interact only with their nearest neighbors through the pair potential that depends on the molecule orientations. It is known that in the homogeneous system there is a direct second-order transition from the isotropic to the biaxial nematic phase, but properties of confined systems are less known. In the present paper the lattice has periodic boundary conditions in the X and Y directions and it has two walls with planar anchoring, perpendicular to the Z directio…
Bistable director alignments of nematic liquid crystals confined in frustrated substrates
利用Lebwohl-Lasher自旋模型的蒙特卡罗模拟，研究了双阻挫面约束下的液晶的面内取向。表面制备有定向棋盘图案，在其上指向矢场被局部锚定为平面但相邻块之间正交。我们发现体中的指向矢场倾向于沿着棋盘图案的对角轴对齐，如实验所报道的[J. H. Kim等人，应用物理信函78，3055（2001）]。当系统达到各向同性-相变温度时，两个稳定取向之间的能垒增加。基于弹性理论，我们发现这种双稳性是由于阻挫面附近指向矢场的空间调制。随着嵌段尺寸的增加和/或弹性模量的减小，指向矢不均匀性的程度增加，从而增大了能垒。我们还发现，稳定状态之间的切换率降低时，块的大小是可比的细胞厚度。
