Xuewei Zhao , Liwenying Yang , Dan Peng , Run-Ran Liu , Ming Li
{"title":"无标度网络上有限尺度的渗流","authors":"Xuewei Zhao , Liwenying Yang , Dan Peng , Run-Ran Liu , Ming Li","doi":"10.1016/j.chaos.2025.117076","DOIUrl":null,"url":null,"abstract":"<div><div>Critical phenomena on scale-free networks with a degree distribution <span><math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>∼</mo><msup><mrow><mi>k</mi></mrow><mrow><mo>−</mo><mi>λ</mi></mrow></msup></mrow></math></span> exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify two distinct crossover routes to mean-field behavior: one controlled by the degree exponent <span><math><mi>λ</mi></math></span>, the other by the degree cutoff <span><math><mrow><mi>K</mi><mo>∼</mo><msup><mrow><mi>V</mi></mrow><mrow><mi>κ</mi></mrow></msup></mrow></math></span>, where <span><math><mi>V</mi></math></span> is the system size and <span><math><mrow><mi>κ</mi><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span> is the cutoff exponent. Increasing <span><math><mi>λ</mi></math></span> or decreasing <span><math><mi>κ</mi></math></span> suppresses heterogeneity and drives the system toward mean-field behavior, with logarithmic corrections near the marginal case. These findings provide a unified picture of the crossover from heterogeneous to homogeneous criticality. In the crossover regime, we observe rich finite-size phenomena, including the transition from vanishing to divergent susceptibility, distinct exponents for the shift and fluctuation of pseudocritical points, and a numerical clarification of previous theoretical predictions.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117076"},"PeriodicalIF":5.6000,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Finite-size scaling of percolation on scale-free networks\",\"authors\":\"Xuewei Zhao , Liwenying Yang , Dan Peng , Run-Ran Liu , Ming Li\",\"doi\":\"10.1016/j.chaos.2025.117076\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Critical phenomena on scale-free networks with a degree distribution <span><math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>∼</mo><msup><mrow><mi>k</mi></mrow><mrow><mo>−</mo><mi>λ</mi></mrow></msup></mrow></math></span> exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify two distinct crossover routes to mean-field behavior: one controlled by the degree exponent <span><math><mi>λ</mi></math></span>, the other by the degree cutoff <span><math><mrow><mi>K</mi><mo>∼</mo><msup><mrow><mi>V</mi></mrow><mrow><mi>κ</mi></mrow></msup></mrow></math></span>, where <span><math><mi>V</mi></math></span> is the system size and <span><math><mrow><mi>κ</mi><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span> is the cutoff exponent. Increasing <span><math><mi>λ</mi></math></span> or decreasing <span><math><mi>κ</mi></math></span> suppresses heterogeneity and drives the system toward mean-field behavior, with logarithmic corrections near the marginal case. These findings provide a unified picture of the crossover from heterogeneous to homogeneous criticality. In the crossover regime, we observe rich finite-size phenomena, including the transition from vanishing to divergent susceptibility, distinct exponents for the shift and fluctuation of pseudocritical points, and a numerical clarification of previous theoretical predictions.</div></div>\",\"PeriodicalId\":9764,\"journal\":{\"name\":\"Chaos Solitons & Fractals\",\"volume\":\"200 \",\"pages\":\"Article 117076\"},\"PeriodicalIF\":5.6000,\"publicationDate\":\"2025-08-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chaos Solitons & Fractals\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0960077925010896\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos Solitons & Fractals","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0960077925010896","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Finite-size scaling of percolation on scale-free networks
Critical phenomena on scale-free networks with a degree distribution exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify two distinct crossover routes to mean-field behavior: one controlled by the degree exponent , the other by the degree cutoff , where is the system size and is the cutoff exponent. Increasing or decreasing suppresses heterogeneity and drives the system toward mean-field behavior, with logarithmic corrections near the marginal case. These findings provide a unified picture of the crossover from heterogeneous to homogeneous criticality. In the crossover regime, we observe rich finite-size phenomena, including the transition from vanishing to divergent susceptibility, distinct exponents for the shift and fluctuation of pseudocritical points, and a numerical clarification of previous theoretical predictions.
期刊介绍:
Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.