论文标题
fortuin-kasteleyn ising模型的几何缩放行为在高维度
Geometric scaling behaviors of the Fortuin-Kasteleyn Ising model in high dimensions
论文作者
论文摘要
最近，我们争辩[Chin。物理。 Lett。 $ 39 $，080502（2022）]，同时在fortuin-kasteleyn（fk）随机群集表示中同时展示两个上层临界维度$（d_c = 4，d_p = 6）$。在本文中，我们对FK Ising模型进行了系统的研究，该模型在空间尺寸的高立管晶格上，从5到7 $ d $ d $ d $ d $ d $ d $ d $ d $ d $。我们提供详细的数据分析，以了解关键点和附近各种数量的关键行为。我们的结果清楚地表明，许多数量以$ 4 <d <6 $和$ d \ geq 6 $表现出独特的关键现象，因此强烈支持这样的论点，即$ 6 $也是临界最大的维度。此外，对于每个研究的维度，我们都会观察到两个配置扇区的存在，两个长度尺度以及两个缩放窗口，因此需要两组关键指数来描述这些行为。我们的发现丰富了对伊辛模型中关键现象的理解。
Recently, we argued [Chin. Phys. Lett. $39$, 080502 (2022)] that the Ising model simultaneously exhibits two upper critical dimensions $(d_c=4, d_p=6)$ in the Fortuin-Kasteleyn (FK) random-cluster representation. In this paper, we perform a systematic study of the FK Ising model on hypercubic lattices with spatial dimensions $d$ from 5 to 7, and on the complete graph. We provide a detailed data analysis of the critical behaviors of a variety of quantities at and near the critical points. Our results clearly show that many quantities exhibit distinct critical phenomena for $4 < d < 6$ and $d\geq 6$, and thus strongly support the argument that $6$ is also an upper critical dimension. Moreover, for each studied dimension, we observe the existence of two configuration sectors, two lengthscales, as well as two scaling windows, and thus, two sets of critical exponents are needed to describe these behaviors. Our finding enriches the understanding of the critical phenomena in the Ising model.
