32 citations · 164 across the 20 of their papers we have counts for
20 papers
Percolation in the three-dimensional Ising model
Jinhong Zhu, Tao Chen, Zhiyi Li +2
Geometric representations provide a useful perspective on critical phenomena in the Ising model. In a recent study [Phys. Rev. E 112, 034118 (2025)], we found that the two-dimensio…
Percolation in the two-dimensional Ising model
Tao Chen, Jinhong Zhu, Wei Zhong +2
The study of the Ising model from a percolation perspective has played a significant role in the modern theory of critical phenomena. We consider the celebrated square-lattice Isin…
Universality of the complete-graph Potts model with
Zirui Peng, Sheng Fang, Hao Hu +1
Universality is a fundamental concept in modern physics. For the -state Potts model, the critical exponents are merely determined by the order-parameter symmetry , spatial…
Spatial Optical Simulator for Classical Statistical Models
Song-Tao Yu, Ming-Gen He, Sheng Fang +2
Optical simulators for the Ising model have demonstrated great promise for solving challenging problems in physics and beyond. Here, we develop a spatial optical simulator for a va…
Crossover Finite-Size Scaling Theory and Its Applications in Percolation
Ming Li, Sheng Fang, Jingfang Fan +1
Finite-size scaling (FSS) for a critical phase transition () states that within a window of size , the scaling behavior of any observable in a system of…
Universal Scaling of Gap Dynamics in Percolation
Sheng Fang, Qing Lin, Jun Meng +4
Percolation is a cornerstone concept in physics, providing crucial insights into critical phenomena and phase transitions. In this study, we adopt a kinetic perspective to reveal t…
Logarithmic Finite-Size Scaling of the Four-Dimensional Ising Model
Zhiyi Li, Tianning Xiao, Zongzheng Zhou +2
Field-theoretical calculations predict that, at the upper critical dimension , the finite-size scaling (FSS) behaviors of the Ising model would be modified by multiplicative…
Finite-Size Scaling of the High-Dimensional Ising Model in the Loop Representation
Tianning Xiao, Zhiyi Li, Zongzheng Zhou +2
Besides its original spin representation, the Ising model is known to have the Fortuin-Kasteleyn (FK) bond and loop representations, of which the former was recently shown to exhib…
Interplay of the complete-graph and Gaussian fixed-point asymptotics in finite-size scaling of percolation above the upper critical dimension
Mingzhong Lu, Sheng Fang, Zongzheng Zhou +1
Percolation has two mean-field theories, the Gaussian fixed point (GFP) and the Landau mean-field theory or the complete graph (CG) asymptotics. By large-scale Monte Carlo simulati…
Geometric properties of the complete-graph Ising model in the loop representation
Zhiyi Li, ZongZheng Zhou, Sheng Fang +1
The exact solution of the Ising model on the complete graph (CG) provides an important, though mean-field, insight for the theory of continuous phase transitions. Besides the origi…
Geometric scaling behaviors of the Fortuin-Kasteleyn Ising model in high dimensions
Sheng Fang, Zongzheng Zhou, Youjin Deng
Recently, we argued [Chin. Phys. Lett. , 080502 (2022)] that the Ising model simultaneously exhibits two upper critical dimensions in the Fortuin-Kasteleyn (FK…
Monte Carlo study of duality and the Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional -state clock model in flow representations
Hao Chen, Pengcheng Hou, Sheng Fang +1
The two-dimensional -state clock model for undergoes two Berezinskii-Kosterlitz-Thouless (BKT) phase transitions as temperature decreases. Here we report an extensive…
Backbone and shortest-path exponents of the two-dimensional -state Potts model
Sheng Fang, Da Ke, Wei Zhong +1
We present a Monte Carlo study of the backbone and the shortest-path exponents of the two-dimensional -state Potts model in the Fortuin-Kasteleyn bond representation. We first u…
Logarithmic finite-size scaling of the self-avoiding walk at four dimensions
Sheng Fang, Youjin Deng, Zongzheng Zhou
The -vector spin model, which includes the self-avoiding walk (SAW) as a special case for the limit, has an upper critical dimensionality at four spatial dime…
Two-scale scenario of rigidity percolation of sticky particles
Yuchuan Wang, Sheng Fang, Ning Xu +1
In the presence of attraction, the jamming transition of packings of frictionless particles corresponds to the rigidity percolation. When the range of attraction is long, the distr…
Percolation effects in the Fortuin-Kasteleyn Ising model on the complete graph
Sheng Fang, Zongzheng Zhou, Youjin Deng
The Fortuin-Kasteleyn (FK) random cluster model, which can be exactly mapped from the -state Potts spin model, is a correlated bond percolation model. By extensive Monte Carlo s…
Critical exponents and universal excess cluster number of percolation in four and five dimensions
Zhongjin Zhang, Pengcheng Hou, Sheng Fang +2
We study critical bond percolation on periodic four-dimensional (4D) and five-dimensional (5D) hypercubes by Monte Carlo simulations. By classifying the occupied bonds into branche…
Complete graph and Gaussian fixed point asymptotics in the five-dimensional Fortuin-Kasteleyn Ising model with periodic boundaries
Sheng Fang, Jens Grimm, Zongzheng Zhou +1
We present an extensive Markov-chain Monte Carlo study of the finite-size scaling behavior of the Fortuin-Kasteleyn Ising model on five-dimensional hypercubic lattices with periodi…
Geometric properties of the Fortuin-Kasteleyn representation of the Ising model
Pengcheng Hou, Sheng Fang, Junfeng Wang +2
We present a Monte Carlo study of the Fortuin-Kasteleyn (FK) clusters of the Ising model on the square (2D) and simple-cubic (3D) lattices. The wrapping probability, a dimensionles…
Random-length Random Walks and Finite-size scaling in high dimensions
Zongzheng Zhou, Jens Grimm, Sheng Fang +2
We address a long-standing debate regarding the finite-size scaling of the Ising model in high dimensions, by introducing a random-length random walk model, which we then study rig…