Dos Santos Cícero T G, Vieira André P, Salinas Silvio R, Andrade Roberto F S
Instituto de Física, Universidade Federal da Bahia, 40170-115 Salvador, Brazil.
Instituto Federal de Educação, Ciência e Tecnologia do Sertão Pernambucano, 56302-100 Petrolina, Brazil.
Phys Rev E. 2021 Mar;103(3-1):032111. doi: 10.1103/PhysRevE.103.032111.
The Maier-Saupe-Zwanzig model for the nematic phase transitions in liquid crystals is investigated in a diamond hierarchical lattice. The model takes into account a parameter to describe the biaxiality of the microscopic units. Also, a suitably chosen external field is added to the Hamiltonian to allow the determination of critical parameters associated with the nematic phase transitions. Using the transfer-matrix technique, the free energy and its derivatives are obtained in terms of recursion relations between successive generations of the hierarchical lattice. In addition, a real-space renormalization-group approach is developed to obtain the critical parameters of the same model system. Results of both methods are in excellent agreement. There are indications of two continuous phase transitions. One of them corresponds to a uniaxial-isotropic transition, in the class of universality of the three-state Potts model on the diamond hierarchical lattice. The transition between the biaxial and the uniaxial phases is in the universality class of the Ising model on the same lattice.
在金刚石分层晶格中研究了用于液晶向列相转变的迈尔 - 绍普 - 茨万齐格模型。该模型考虑了一个描述微观单元双轴性的参数。此外，在哈密顿量中添加了一个适当选择的外场，以便确定与向列相转变相关的临界参数。使用转移矩阵技术，根据分层晶格连续世代之间的递归关系获得自由能及其导数。此外，还开发了一种实空间重整化群方法来获得同一模型系统的临界参数。两种方法的结果非常吻合。有迹象表明存在两个连续相变。其中一个对应于单轴 - 各向同性转变，属于金刚石分层晶格上三态Potts模型的普适类。双轴相和单轴相之间的转变属于同一晶格上伊辛模型的普适类。
