de Gennes区域下RNA模型的拓扑相变
Topological phase transition in a RNA model in the de Gennes regime
摘要：
我们研究了G. Vernizzi，H. Orland和A.在溶液中强正离子浓度范围内的Zee。该模型考虑了一个柔性链的平等基地，可以成对地与任何其他一个沿链相互作用，同时保持饱和的相互作用的属性。在所考虑的区域中，我们观察到分离两相的临界温度T_c的出现，该临界温度T_c可以由主导构型的拓扑结构来表征：在大的温度范围内，分子的主要构型具有非常大的分布，（分子大小的数量级），对应于复杂的拓扑结构，而在相反的低温状态下，主要的配置是简单的并且具有球形拓扑。我们确定了这种拓扑相变是一级相变，并给出了T_c的解析表达式。该模型研究的区域与de Gennes研究的致密聚合物系统相似
英文摘要：
We study a simplified model of the RNA molecule proposed by G. Vernizzi, H. Orland and A. Zee in the regime of strong concentration of positive ions in solution. The model considers a flexible chain of equal bases that can pairwise interact with any other one along the chain, while preserving the property of saturation of the interactions. In the regime considered, we observe the emergence of a critical temperature T_c separating two phases that can be characterized by the topology of the predominant configurations: in the large temperature regime, the dominant configurations of the molecule have very large genera (of the order of the size of the molecule), corresponding to a complex topology, whereas in the opposite regime of low temperatures, the dominant configurations are simple and have the topology of a sphere. We determine that this topological phase transition is of first order and provide an analytic expression for T_c. The regime studied for this model exhibits analogies with that for the dense polymer systems studied by de Gennes
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