Universality of percolation at dynamic pseudocritical point

doi:10.1088/1674-1056/adaccf

中国物理B ›› 2025, Vol. 34 ›› Issue (4): 40501-040501.doi: 10.1088/1674-1056/adaccf

Universality of percolation at dynamic pseudocritical point

Qiyuan Shi(石骐源)¹, Shuo Wei(魏硕)¹, Youjin Deng(邓友金)^2,1,3,†, and Ming Li(李明)^4,‡

1 Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;
2 Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China;
3 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China;
4 School of Physics, Hefei University of Technology, Hefei 230009, ChinaResearch Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China;
3 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China;
4 School of Physics, Hefei University of Technology, Hefei 230009, China

收稿日期:2024-12-14 修回日期:2025-01-12 接受日期:2025-01-22 出版日期:2025-04-15 发布日期:2025-04-15
通讯作者: Youjin Deng E-mail:yjdeng@ustc.edu.cn;lim@hfut.edu.cn
基金资助:
The authors acknowledge helpful discussions with Jingfang Fan. The research was supported by the National Natural Science Foundation of China (Grant No. 12275263), the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0301900), and Natural Science Foundation of Fujian Province of China (Grant No. 2023J02032).

Universality of percolation at dynamic pseudocritical point

Qiyuan Shi(石骐源)¹, Shuo Wei(魏硕)¹, Youjin Deng(邓友金)^2,1,3,†, and Ming Li(李明)^4,‡

1 Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;
2 Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China;
3 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China;
4 School of Physics, Hefei University of Technology, Hefei 230009, ChinaResearch Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China;
3 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China;
4 School of Physics, Hefei University of Technology, Hefei 230009, China

Received:2024-12-14 Revised:2025-01-12 Accepted:2025-01-22 Online:2025-04-15 Published:2025-04-15
Contact: Youjin Deng E-mail:yjdeng@ustc.edu.cn;lim@hfut.edu.cn
Supported by:
The authors acknowledge helpful discussions with Jingfang Fan. The research was supported by the National Natural Science Foundation of China (Grant No. 12275263), the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0301900), and Natural Science Foundation of Fujian Province of China (Grant No. 2023J02032).

摘要/Abstract

摘要： Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point. Focusing on two-dimensional percolation, we show that the size distribution of the largest cluster asymptotically approaches to a Gumbel form in the subcritical phase, a Gaussian form in the supercritical phase, and transitions within the critical finite-size scaling window. Numerical results indicate that, at consistently defined pseudocritical points, this distribution exhibits a universal form across various lattices and percolation models (bond or site), within error bars, yet differs from the distribution at the critical point. The critical polynomial, universally zero for two-dimensional percolation at the critical point, becomes nonzero at pseudocritical points. Nevertheless, numerical evidence suggests that the critical polynomial, along with other dimensionless quantities such as wrapping probabilities and Binder cumulants, assumes fixed values at the pseudocritical point that are independent of the percolation type (bond or site) but vary with lattice structures. These findings imply that while strict universality breaks down at the pseudocritical point, certain extreme-value statistics and dimensionless quantities exhibit quasi-universality, revealing a subtle connection between scaling behaviors at critical and pseudocritical points.

关键词: percolation, universality, extreme-value statistics, pseudocritical point

Abstract: Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point. Focusing on two-dimensional percolation, we show that the size distribution of the largest cluster asymptotically approaches to a Gumbel form in the subcritical phase, a Gaussian form in the supercritical phase, and transitions within the critical finite-size scaling window. Numerical results indicate that, at consistently defined pseudocritical points, this distribution exhibits a universal form across various lattices and percolation models (bond or site), within error bars, yet differs from the distribution at the critical point. The critical polynomial, universally zero for two-dimensional percolation at the critical point, becomes nonzero at pseudocritical points. Nevertheless, numerical evidence suggests that the critical polynomial, along with other dimensionless quantities such as wrapping probabilities and Binder cumulants, assumes fixed values at the pseudocritical point that are independent of the percolation type (bond or site) but vary with lattice structures. These findings imply that while strict universality breaks down at the pseudocritical point, certain extreme-value statistics and dimensionless quantities exhibit quasi-universality, revealing a subtle connection between scaling behaviors at critical and pseudocritical points.

Key words: percolation, universality, extreme-value statistics, pseudocritical point

中图分类号: (Classical statistical mechanics)

05.20.-y

05.10.Ln (Monte Carlo methods) 64.60.ah (Percolation)

Qiyuan Shi(石骐源), Shuo Wei(魏硕), Youjin Deng(邓友金), and Ming Li(李明). Universality of percolation at dynamic pseudocritical point[J]. 中国物理B, 2025, 34(4): 40501-040501.

Qiyuan Shi(石骐源), Shuo Wei(魏硕), Youjin Deng(邓友金), and Ming Li(李明). Universality of percolation at dynamic pseudocritical point[J]. Chin. Phys. B, 2025, 34(4): 40501-040501.

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Universality of percolation at dynamic pseudocritical point

Universality of percolation at dynamic pseudocritical point

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