二维液晶的临界行为
On the critical behavior of two-dimensional liquid crystals
摘要：
Lebwohl-Lasher（LL）模型是描述实际液晶向列相-各向同性相变的传统模型。本文对二维LL模型的温度行为和有限尺寸标度进行了数值研究。我们讨论两种可能的情况。在第一个模型中，二维LL模型呈现出与二维XY模型中出现的拓扑转变类似的相变。在第二个中，2D LL模型没有表现出任何临界转变，但其低温行为的特征在于在零温度下从无序相到有序相的交叉。我们实现和讨论各种比较与二维XY模型和二维海森堡模型。在前人对序参量的有限尺寸标度行为和序参量轮廓的共形映射研究的基础上，我们分析了概率分布函数的临界标度、超标度关系和刚度序参量，并得出结论：第二种情况（无临界转变）是最合理的。
英文摘要：
The Lebwohl-Lasher (LL) model is the traditional model used to describe the nematic-isotropic transition of real liquid crystals. In this paper, we develop a numerical study of the temperature behaviour and of finite-size scaling of the two-dimensional (2D) LL-model. We discuss two possible scenarios. In the first one, the 2D LL-model presents a phase transition similar to the topological transition appearing in the 2D XY-model. In the second one, the 2D LL-model does not exhibit any critical transition, but its low temperature behaviour is rather characterized by a crossover from a disordered phase to an ordered phase at zero temperature. We realize and discuss various comparisons with the 2D XY-model and the 2D Heisenberg model. Adding to previous studies of finite-size scaling behaviour of the order parameter and conformal mapping of order parameter profile, we analyze the critical scaling of the probability distribution function, hyperscaling relations and stiffness order parameter and conclude that the second scenario (no critical transition) is the most plausible.
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