曲率消失鞍点诱导的相变
Phase transitions induced by saddle points of vanishing curvature
摘要：
基于对一般经典多粒子系统势能面鞍点的研究，提出了热力学相变发生的一个必要判据。值得注意的是，这一准则对微观性质施加了条件，即势能鞍点处的曲率，并将它们与相变的宏观现象联系起来。我们将我们的结果应用到两个完全可解的模型，证实了所得出的标准不仅是有效的，但也尖锐和有用的：对于这两个模型的研究，该标准排除了相变的所有值的势能，但过渡能的发生。这一结果增加了一个几何成分，以建立一个拓扑条件的发生相变，从而提供了一个答案，长期存在的问题，其中拓扑结构的变化，在配置空间可以诱导相变。
英文摘要：
Based on the study of saddle points of the potential energy landscapes of generic classical many-particle systems, we present a necessary criterion for the occurrence of a thermodynamic phase transition. Remarkably, this criterion imposes conditions on microscopic properties, namely curvatures at the saddle points of the potential, and links them to the macroscopic phenomenon of a phase transition. We apply our result to two exactly solvable models, corroborating that the criterion derived is not only valid, but also sharp and useful: For both models studied, the criterion excludes the occurrence of a phase transition for all values of the potential energy but the transition energy. This result adds a geometrical ingredient to an established topological condition for the occurrence of a phase transition, thereby providing an answer to the long standing question of which topology changes in configuration space can induce a phase transition.
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