论文标题
在范德华-KAC极限中的液晶的列式一阶相变
Nematic first order phase transition for liquid crystals in the van der Waals-Kac limit
论文作者
论文摘要
在本文中，我们重新审视并扩展了Onsager液晶理论的一些数学方面，这些方面近年来已经由不同的社区（统计力学，分析和概率）进行了研究。我们引入了一种各向异性分子的模型，其三维取向通过KAC型相互作用相互作用。我们证明，在热力学极限之后将相互作用范围发送到无穷大的极限，自由能趋向于有效的能量功能的最大效果。然后，我们证明，如果角相互作用的球形谐波变换具有负最小值，则随着系统的总密度的增加，该有效的自由能功能将显示一阶相变。
In this paper we revisit and extend some mathematical aspects of Onsager's theory of liquid crystals that have been investigated in recent years by different communities (statistical mechanics, analysis and probability). We introduce a model of anisotropic molecules with three-dimensional orientations interacting via a Kac-type interaction. We prove that, in the limit in which the range of the interaction is sent to infinity after the thermodynamic limit, the free energy tends to the infimum of an effective energy functional à la Onsager. We then prove that, if the spherical harmonic transform of the angular interaction has a negative minimum, this effective free energy functional displays a first order phase transition as the total density of the system increases.
