{"title":"具有异质度分布的平面随机网格上的非普遍临界动力学","authors":"","doi":"10.1016/j.physa.2024.130047","DOIUrl":null,"url":null,"abstract":"<div><p>The weighted planar stochastic (WPS) lattice introduces a topological disorder that emerges from a multifractal structure. Its dual network has a power-law degree distribution and is embedded in a two-dimensional space, forming a planar network. We modify the original recipe to construct WPS networks with degree distributions interpolating smoothly between the original power-law tail, <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow><mo>∼</mo><msup><mrow><mi>q</mi></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msup></mrow></math></span> with exponent <span><math><mrow><mi>α</mi><mo>≈</mo><mn>5</mn><mo>.</mo><mn>6</mn></mrow></math></span>, and a square lattice. We analyze the role of the disorder in the modified WPS model, considering the critical behavior of the contact process (CP). We report a critical scaling depending on the network degree distribution. The scaling exponents differ from the standard mean-field behavior reported for CP on infinite-dimensional (random) graphs with power-law degree distribution. Furthermore, the disorder present in the WPS lattice model is in agreement with the Luck-Harris criterion for the relevance of disorder in critical dynamics. However, despite the same wandering exponent <span><math><mrow><mi>ω</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math></span>, the disorder effects observed for the WPS lattice are weaker than those found for uncorrelated disorder.</p></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":null,"pages":null},"PeriodicalIF":2.8000,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nonuniversal critical dynamics on planar random lattices with heterogeneous degree distributions\",\"authors\":\"\",\"doi\":\"10.1016/j.physa.2024.130047\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The weighted planar stochastic (WPS) lattice introduces a topological disorder that emerges from a multifractal structure. Its dual network has a power-law degree distribution and is embedded in a two-dimensional space, forming a planar network. We modify the original recipe to construct WPS networks with degree distributions interpolating smoothly between the original power-law tail, <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow><mo>∼</mo><msup><mrow><mi>q</mi></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msup></mrow></math></span> with exponent <span><math><mrow><mi>α</mi><mo>≈</mo><mn>5</mn><mo>.</mo><mn>6</mn></mrow></math></span>, and a square lattice. We analyze the role of the disorder in the modified WPS model, considering the critical behavior of the contact process (CP). We report a critical scaling depending on the network degree distribution. The scaling exponents differ from the standard mean-field behavior reported for CP on infinite-dimensional (random) graphs with power-law degree distribution. Furthermore, the disorder present in the WPS lattice model is in agreement with the Luck-Harris criterion for the relevance of disorder in critical dynamics. However, despite the same wandering exponent <span><math><mrow><mi>ω</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math></span>, the disorder effects observed for the WPS lattice are weaker than those found for uncorrelated disorder.</p></div>\",\"PeriodicalId\":20152,\"journal\":{\"name\":\"Physica A: Statistical Mechanics and its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2024-08-19\",\"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/S0378437124005569\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica A: Statistical Mechanics and its Applications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378437124005569","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}
Nonuniversal critical dynamics on planar random lattices with heterogeneous degree distributions
The weighted planar stochastic (WPS) lattice introduces a topological disorder that emerges from a multifractal structure. Its dual network has a power-law degree distribution and is embedded in a two-dimensional space, forming a planar network. We modify the original recipe to construct WPS networks with degree distributions interpolating smoothly between the original power-law tail, with exponent , and a square lattice. We analyze the role of the disorder in the modified WPS model, considering the critical behavior of the contact process (CP). We report a critical scaling depending on the network degree distribution. The scaling exponents differ from the standard mean-field behavior reported for CP on infinite-dimensional (random) graphs with power-law degree distribution. Furthermore, the disorder present in the WPS lattice model is in agreement with the Luck-Harris criterion for the relevance of disorder in critical dynamics. However, despite the same wandering exponent , the disorder effects observed for the WPS lattice are weaker than those found for uncorrelated disorder.
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.