{"title":"Describing self-organized criticality as a continuous phase transition.","authors":"S S Manna","doi":"10.1103/PhysRevE.111.024111","DOIUrl":null,"url":null,"abstract":"<p><p>Can the concept of self-organized criticality, exemplified by models such as the sandpile model, be described within the framework of continuous phase transitions? In this paper, we provide extensive numerical evidence supporting an affirmative answer. Specifically, we explore the Bak, Tang, and Wiesenfeld (BTW) and Manna sandpile models as instances of percolation transitions from disordered to ordered phases. To facilitate this analysis, we introduce the concept of drop density-a continuously adjustable control variable that quantifies the average number of particles added to a site. By tuning this variable, we observe a transition in the sandpile from a subcritical to a critical phase. Additionally, we define the scaled size of the largest avalanche occurring from the beginning of the sandpile as the order parameter for the self-organized critical transition and analyze its scaling behavior. Furthermore, we calculate the correlation length exponent and note its divergence as the critical point is approached. The finite-size scaling analysis of the avalanche size distribution works quite well at the critical point of the BTW sandpile.</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"111 2-1","pages":"024111"},"PeriodicalIF":2.2000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/PhysRevE.111.024111","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, FLUIDS & PLASMAS","Score":null,"Total":0}
引用次数: 0
Abstract
Can the concept of self-organized criticality, exemplified by models such as the sandpile model, be described within the framework of continuous phase transitions? In this paper, we provide extensive numerical evidence supporting an affirmative answer. Specifically, we explore the Bak, Tang, and Wiesenfeld (BTW) and Manna sandpile models as instances of percolation transitions from disordered to ordered phases. To facilitate this analysis, we introduce the concept of drop density-a continuously adjustable control variable that quantifies the average number of particles added to a site. By tuning this variable, we observe a transition in the sandpile from a subcritical to a critical phase. Additionally, we define the scaled size of the largest avalanche occurring from the beginning of the sandpile as the order parameter for the self-organized critical transition and analyze its scaling behavior. Furthermore, we calculate the correlation length exponent and note its divergence as the critical point is approached. The finite-size scaling analysis of the avalanche size distribution works quite well at the critical point of the BTW sandpile.
以沙堆模型等模型为例的自组织临界性的概念能否在连续相变的框架内描述?在本文中,我们提供了广泛的数字证据来支持肯定的答案。具体来说,我们探讨了Bak, Tang, and Wiesenfeld (BTW)和Manna砂堆模型作为渗流从无序阶段到有序阶段转变的实例。为了便于分析,我们引入了水滴密度的概念——一个连续可调的控制变量,量化了添加到一个位点的平均颗粒数量。通过调整这个变量,我们观察到砂堆从亚临界阶段到临界阶段的转变。此外,我们定义了自组织临界转变的序参量为自组织临界转变的尺度大小,并分析了其尺度行为。此外,我们计算了相关长度指数,并记录了其在接近临界点时的发散度。雪崩粒径分布的有限尺度尺度分析在BTW砂堆临界点处效果较好。
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.