Peng Zirui, Fang Sheng, Hu Hao, Deng Youjin
University of Science and Technology of China, Department of Modern Physics,, Hefei, Anhui 230026, China.
University of Science and Technology of China, Hefei National Research Center for Physical Sciences at the Microscales, Hefei, Anhui 230026, China.
Phys Rev E. 2025 May;111(5-1):054134. doi: 10.1103/PhysRevE.111.054134.
Universality is a fundamental concept in modern physics. For the q-state Potts model, the critical exponents are merely determined by the order-parameter symmetry S_{q}, spatial dimensionality and interaction range, independent of microscopic details. In a simplest and mean-field treatment, i.e., the Potts model on complete graph (CG), the phase transition is further established to be of percolation universality for the range of 0<q<2. By simulating the CG Potts model in the random-cluster representation, we numerically demonstrate such a hyperuniversality that the critical exponents are the same for 0<q<2 and, moreover, the Ising system (q=2) exhibits a variety of critical geometric properties in percolation universality. On the other hand, many other universal properties in the finite-size scaling (FSS) theory, including Binder-like ratios and distribution function of the order parameter, are observed to be q dependent. Meanwhile, we have made improvements to the Monte Carlo algorithms for efficiently simulating the CG Potts model. Our finding provides valuable insights for the study of critical phenomena in finite spatial dimensions, particularly when the FSS theory is utilized.
普遍性是现代物理学中的一个基本概念。对于q态Potts模型，临界指数仅由序参量对称性(S_{q})、空间维度和相互作用范围决定，与微观细节无关。在最简单的平均场处理中，即在完全图（CG）上的Potts模型中，对于(0<q<2)的范围，进一步确定相变具有渗流普遍性。通过在随机簇表示中模拟CG Potts模型，我们通过数值证明了这种超普遍性，即对于(0<q<2)，临界指数是相同的，此外，伊辛系统（(q = 2)）在渗流普遍性中表现出各种临界几何性质。另一方面，在有限尺寸标度（FSS）理论中的许多其他普遍性质，包括类似Binder的比率和序参量的分布函数，被观察到与q有关。同时，我们对蒙特卡罗算法进行了改进，以有效地模拟CG Potts模型。我们的发现为有限空间维度中的临界现象研究提供了有价值的见解，特别是在使用FSS理论时。
