We use a simple statistical model to investigate the effects of an applied magnetic field and of the dilution of site elements on the phase diagrams of biaxial nematic systems, with an emphasis on the stability of the Landau multicritical point. The statistical lattice model consists of intrinsically biaxial nematogenic units, which interact via a Maier–Saupe potential, and which are characterized by a discrete choice of orientations of the microscopic nematic directors. According to previous calculations at zero field and in the absence of dilution, we regain the well-known sequence of biaxial, uniaxial, and disordered structures as the temperature is increased, and locate the Landau point. We then focus on the topological changes induced in the phase diagram by the application of an external magnetic field, and show that the Landau point is destabilized by the presence of an applied field. On the other hand, in the absence of a field, we show that only a quite strong dilution of nematic sites is capable of destabilizing the Landau point.

中文翻译：

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磁场和稀释作用对向列双轴系统简单统计模型相图的影响

我们使用一个简单的统计模型来研究施加的磁场和位点元素稀释对双轴向列系统相图的影响，重点是Landau多临界点的稳定性。统计晶格模型由固有的双轴杀线虫单元组成，这些单元通过Maier-Saupe势相互作用，并且具有微观向列相向矢状体的离散选择。根据先前在零场且没有稀释的情况下的计算，随着温度升高，我们重新获得了众所周知的双轴，单轴和无序结构序列，并找到了Landau点。然后，我们将重点研究通过施加外部磁场在相图中引起的拓扑变化，并表明，由于存在外加电场，Landau点不稳定。另一方面，在没有田野的情况下，我们证明只有向列位点的强烈稀释才能破坏朗道点的稳定性。