Papers › Percolation in the two-dimensional Ising model
Percolation in the two-dimensional Ising model
Tao Chen, Jinhong Zhu, Wei Zhong, Sheng Fang, Youjin Deng
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
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 Ising model and construct percolation clusters by placing bonds, with probability p, between any pair of parallel spins within an extended range beyond nearest neighbors. At the Ising criticality, we observe two percolation transitions as p increases: starting from a disordered phase with only small clusters, the percolation system enters into a stable critical phase that persists over a wide range p_(c₁) < p < p_(c₂), and then develops a long-ranged percolation order with giant clusters for both up and down spins. At p_(c1) and for the stable critical phase, the critical behaviors agree well with those for the Fortuin-Kasteleyn random clusters and the spin domains of the Ising model, respectively. At p_(c2), the fractal dimension of clusters and the scaling exponent along p direction are estimated as yₕ₂ = 1.958 0(6) and yₚ₂ = 0.552(9), of which the exact values remain unknown. These findings reveal interesting geometric properties of the two-dimensional Ising model that has been studied for more than 100 years.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections