论文标题
Ising模型的几何临界维度
Geometric Upper Critical Dimensions of the Ising Model
论文作者
论文摘要
已知Ising模型的上部临界维度为$ d_c = 4 $，高于该临界行为被认为是微不足道的。我们在此论证了广泛的模拟，即在随机群集表示中，Ising模型同时在$（d_c = 4，d_p = 6）$（d_c = 4，d_p = 6）$中表现出两个上层临界维度，而$ d \ geq d_p $的关键簇（除了最大的一个，一个最大的geq d_p $），由percolation forcolation customity offcolation customential offcolation custical offcolation customationallationallation。我们预测各种各样的几何特性，然后在4到7的维度和完整的图中提供有力的证据。我们的发现大大提高了对Ising模型的理解，这是许多物理学分支中的基本系统。
The upper critical dimension of the Ising model is known to be $d_c=4$, above which critical behavior is regarded as trivial. We hereby argue from extensive simulations that, in the random-cluster representation, the Ising model simultaneously exhibits two upper critical dimensions at $(d_c= 4, d_p=6)$, and critical clusters for $d \geq d_p$, except the largest one, are governed by exponents from percolation universality. We predict a rich variety of geometric properties and then provide strong evidence in dimensions from 4 to 7 and on complete graphs. Our findings significantly advance the understanding of the Ising model, which is a fundamental system in many branches of physics.
