完全超图上生成超森林模型的相变
Phase transition in the spanning-hyperforest model on complete hypergraphs
摘要：
利用新的Grassmann公式研究了k一致完全超图的生成超森林模型的相变，其中k>= 2. k=2的情况在完全图上简化为生成森林模型。不同的k一次研究通过使用微正则系综，其中超森林的数量是固定的。低温阶段的特点是出现了一个巨大的超森林。相变发生在超森林的数量是顶点总数的分数（k-1）/k时。在临界状态下的行为也通过两个鞍点的合并进行了研究。由于Grassmann公式具有全局超对称性，我们证明了相变是二级的，并且与超对称性破缺有关。通过引入显式破缺场，我们探索了低温下的纯晶相。
英文摘要：
By using our novel Grassmann formulation we study the phase transition of the spanning-hyperforest model of the k-uniform complete hypergraph for any k>= 2. The case k=2 reduces to the spanning-forest model on the complete graph. Different k are studied at once by using a microcanonical ensemble in which the number of hyperforests is fixed. The low-temperature phase is characterized by the appearance of a giant hyperforest. The phase transition occurs when the number of hyperforests is a fraction (k-1)/k of the total number of vertices. The behaviour at criticality is also studied by means of the coalescence of two saddle points. As the Grassmann formulation exhibits a global supersymmetry we show that the phase transition is second order and is associated to supersymmetry breaking and we explore the pure thermodynamical phase at low temperature by introducing an explicit breaking field.
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