172 citations · 455 across the 23 of their papers we have counts for
19 papers · 1 filter
Self-avoiding trails in two and three dimensions
Xiaodi Su, Zongzheng Zhou, Qianqian Wu
The self-avoiding trail is an important variant of the self-avoiding walk. In this work, we employ an irreversible Markov chain Monte Carlo algorithm, together with the reversible…
Correction-to-scaling exponent for percolation and the Fortuin--Kasteleyn Potts model in two dimensions
Yihao Xu, Tao Chen, Zongzheng Zhou +2
The number of clusters (per site) of size , a central quantity in percolation theory, displays at criticality an algebraic scaling behavior of the form $n_s\simeq s^{-τ}\,…
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…
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…
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…
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…
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…
Geometric explanation of anomalous finite-size scaling in high dimensions
Jens Grimm, Eren Metin Elçi, Zongzheng Zhou +2
We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Is…
Leaf-excluded percolation in two and three dimensions
Zongzheng Zhou, Xiao Xu, Timothy M. Garoni +1
We introduce the \emph{leaf-excluded} percolation model, which corresponds to independent bond percolation conditioned on the absence of leaves (vertices of degree one). We study t…
Geometric structure of percolation clusters
Xiao Xu, Junfeng Wang, Zongzheng Zhou +2
We investigate the geometric properties of percolation clusters, by studying square-lattice bond percolation on the torus. We show that the density of bridges and nonbridges both t…
Bond and Site Percolation in Three Dimensions
Junfeng Wang, Zongzheng Zhou, Wei Zhang +2
We simulate the bond and site percolation models on a simple-cubic lattice with linear sizes up to L=512, and estimate the percolation thresholds to be $p_c ({\rm bond})=0.248\,811…
High-precision Monte Carlo study of directed percolation in (d+1) dimensions
Junfeng Wang, Zongzheng Zhou, Qingquan Liu +2
We present a Monte Carlo study of the bond and site directed (oriented) percolation models in dimensions on simple-cubic and body-centered-cubic lattices, with $2 \leq d \l…
Shortest-Path Fractal Dimension for Percolation in Two and Three Dimensions
Zongzheng Zhou, Ji Yang, Youjin Deng +1
We carry out a high-precision Monte Carlo study of the shortest-path fractal dimension $\dm$ for percolation in two and three dimensions, using the Leath-Alexandrowicz method which…
Crossover from Isotropic to Directed Percolation
Zongzheng Zhou, Ji Yang, Robert M. Ziff +1
We generalize the directed percolation (DP) model by relaxing the strict directionality of DP such that propagation can occur in either direction but with anisotropic probabilities…
Autocorrelations in the totally asymmetric simple exclusion process and Nagel-Schreckenberg model
Jan de Gier, Timothy M. Garoni, Zongzheng Zhou
We study via Monte Carlo simulation the dynamics of the Nagel-Schreckenberg model on a finite system of length L with open boundary conditions and parallel updates. We find numeric…