Lattice models for liquid crystals
Lattice models for liquid crystals
复制标题
液晶晶格模型
DOI：
--
复制
发表时间：
1979
期刊：
影响因子：
--
通讯作者：
E. Lieb
中科院分区：
文献类型：
--
作者：
O. J. Heilmann;E. Lieb
液晶理论中的一个问题是如何建立一个模型系统，使其在低温下显示长程取向有序，而不是在所有方向上显示平动有序。我们提出了具有吸引相互作用的硬核粒子的五种晶格模型（两个二维和三个三维），并证明（使用反射正性和佩尔斯论证）它们在低温下具有取向顺序；如果不存在吸引相互作用，二维模型就没有这种排序。我们不能证明这些模型不具有完全的平动秩序，但它们的零温度状态使我们推测完全平动秩序总是不存在的。
A problem in the theory of liquid crystals is to construct a model system which at low temperatures displays long-range orientational order, but not translational order in all directions. We present five lattice models (two two-dimensional and three three-dimensional) of hard-core particles with attractive interactions and prove (using reflection positivity and the Peierls argument) that they have orientational order at low temperatures; the two-dimensional models have no such ordering if the attractive interaction is not present. We cannot prove that these models do not have complete translational order, but their zero-temperature states are such that we are led to conjecture that complete translational order is always absent.