{"title":"Independence role in the generalized Sznajd model","authors":"","doi":"10.1016/j.physa.2024.130042","DOIUrl":null,"url":null,"abstract":"<div><p>The Sznajd model is one of sociophysics’s well-known opinion dynamics models. Based on social validation, it has found application in diverse social systems and remains an intriguing subject of study, particularly in scenarios where interacting agents deviate from prevailing norms. This paper investigates the generalized Sznajd model, featuring independent agents on a complete graph and a two-dimensional square lattice. Agents in the network act independently with a probability <span><math><mi>p</mi></math></span>, signifying a change in their opinion or state without external influence. This model defines a paired agent size <span><math><mi>r</mi></math></span>, influencing a neighboring agent size <span><math><mi>n</mi></math></span> to adopt their opinion. This study incorporates analytical and numerical approaches, especially on the complete graph. Our results show that the macroscopic state of the system remains unaffected by the neighbor size <span><math><mi>n</mi></math></span> but is contingent solely on the number of paired agents <span><math><mi>r</mi></math></span>. Additionally, the time required to reach a stationary state is inversely proportional to the number of neighboring agents <span><math><mi>n</mi></math></span>. For the two-dimensional square lattice, two critical points <span><math><mrow><mi>p</mi><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math></span> emerge based on the configuration of agents. The results indicate that the universality class of the model on the complete graph aligns with the mean-field Ising universality class. Furthermore, the universality class of the model on the two-dimensional square lattice, featuring two distinct configurations, is identical and falls within the two-dimensional Ising universality class.</p></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":null,"pages":null},"PeriodicalIF":2.8000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica A: Statistical Mechanics and its Applications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S037843712400551X","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The Sznajd model is one of sociophysics’s well-known opinion dynamics models. Based on social validation, it has found application in diverse social systems and remains an intriguing subject of study, particularly in scenarios where interacting agents deviate from prevailing norms. This paper investigates the generalized Sznajd model, featuring independent agents on a complete graph and a two-dimensional square lattice. Agents in the network act independently with a probability , signifying a change in their opinion or state without external influence. This model defines a paired agent size , influencing a neighboring agent size to adopt their opinion. This study incorporates analytical and numerical approaches, especially on the complete graph. Our results show that the macroscopic state of the system remains unaffected by the neighbor size but is contingent solely on the number of paired agents . Additionally, the time required to reach a stationary state is inversely proportional to the number of neighboring agents . For the two-dimensional square lattice, two critical points emerge based on the configuration of agents. The results indicate that the universality class of the model on the complete graph aligns with the mean-field Ising universality class. Furthermore, the universality class of the model on the two-dimensional square lattice, featuring two distinct configurations, is identical and falls within the two-dimensional Ising universality class.
Sznajd 模型是社会物理学著名的舆论动力学模型之一。它以社会验证为基础,在各种社会系统中都有应用,尤其是在互动主体偏离普遍规范的情况下,它仍然是一个引人入胜的研究课题。本文研究的是广义 Sznajd 模型,其特点是在完整图和二维方格上的独立代理。网络中的代理以概率 p 独立行动,表示其观点或状态在不受外部影响的情况下发生变化。该模型定义了大小为 r 的配对代理,可影响大小为 n 的相邻代理采纳其意见。这项研究结合了分析和数值方法,特别是在完整图上。我们的研究结果表明,系统的宏观状态不受相邻代理大小 n 的影响,而完全取决于配对代理的数量 r。结果表明,该模型在完整图上的普遍性类与均场伊辛普遍性类一致。此外,该模型在二维方格上的普遍性类与二维伊辛普遍性类相同,具有两种不同的配置。
期刊介绍:
Physica A: Statistical Mechanics and its Applications
Recognized by the European Physical Society
Physica A publishes research in the field of statistical mechanics and its applications.
Statistical mechanics sets out to explain the behaviour of macroscopic systems by studying the statistical properties of their microscopic constituents.
Applications of the techniques of statistical mechanics are widespread, and include: applications to physical systems such as solids, liquids and gases; applications to chemical and biological systems (colloids, interfaces, complex fluids, polymers and biopolymers, cell physics); and other interdisciplinary applications to for instance biological, economical and sociological systems.