论文标题
随机常规图上的互换和量子海森堡模型的宏观周期
Macroscopic cycles for the interchange and quantum Heisenberg models on random regular graphs
论文作者
论文摘要
互换过程是一个随机置换模型，作为研究量子海森堡模型的一种方式。对于此模型，在一些特定图表上取得了进展：树，超立方体，锤子图，完整的图形和两个块图。在这里，我们表明，对于足够大的参数，互换过程和量子Heisenberg模型都在随机的D期权图上具有宏观簇。这样的结果仅在完整的图表和两个块图中知道。
The interchange process is a random permutation model that was introduced as a way to study the quantum Heisenberg model. For this model, progress had been made on some specific graphs: trees, the hypercube, the Hamming graph, the complete graph and the two block graph. Here we show that for large enough parameters, both the interchange process and the quantum Heisenberg model have macroscopic clusters on random d-regular graphs. Such a result was only known for the complete graph and the two blocks graph.
