Andrea Gabrielli, Diego Garlaschelli, Subodh P. Patil, M. Ángeles Serrano
{"title":"网络重正化","authors":"Andrea Gabrielli, Diego Garlaschelli, Subodh P. Patil, M. Ángeles Serrano","doi":"10.1038/s42254-025-00817-5","DOIUrl":null,"url":null,"abstract":"The renormalization group (RG) is a powerful theoretical framework. It is used on systems with many degrees of freedom to transform the description of their configurations, along with the associated model parameters and coupling constants, across different levels of resolution. The RG also provides a way to identify critical points of phase transitions and study the system’s behaviour around them. In traditional physical applications, the RG largely builds on the notions of homogeneity, symmetry, geometry and locality to define metric distances, scale transformations and self-similar coarse-graining schemes. More recently, efforts have been made to extend RG concepts to complex networks. However, in such systems, explicit geometric coordinates do not necessarily exist, different nodes and subgraphs can have different statistical properties, and homogeneous lattice-like symmetries are absent — all features that make it complicated to define consistent renormalization procedures. In this Technical Review, we discuss the main approaches, important advances, and the remaining open challenges for network renormalization. The renormalization group (RG) is a theoretical framework to transform systems across scales and identify critical points of phase transitions. In recent years, efforts have extended RG to complex networks, which challenge traditional assumptions. This Technical Review covers key approaches and open challenges.","PeriodicalId":19024,"journal":{"name":"Nature Reviews Physics","volume":"7 4","pages":"203-219"},"PeriodicalIF":44.8000,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Network renormalization\",\"authors\":\"Andrea Gabrielli, Diego Garlaschelli, Subodh P. Patil, M. Ángeles Serrano\",\"doi\":\"10.1038/s42254-025-00817-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The renormalization group (RG) is a powerful theoretical framework. It is used on systems with many degrees of freedom to transform the description of their configurations, along with the associated model parameters and coupling constants, across different levels of resolution. The RG also provides a way to identify critical points of phase transitions and study the system’s behaviour around them. In traditional physical applications, the RG largely builds on the notions of homogeneity, symmetry, geometry and locality to define metric distances, scale transformations and self-similar coarse-graining schemes. More recently, efforts have been made to extend RG concepts to complex networks. However, in such systems, explicit geometric coordinates do not necessarily exist, different nodes and subgraphs can have different statistical properties, and homogeneous lattice-like symmetries are absent — all features that make it complicated to define consistent renormalization procedures. In this Technical Review, we discuss the main approaches, important advances, and the remaining open challenges for network renormalization. The renormalization group (RG) is a theoretical framework to transform systems across scales and identify critical points of phase transitions. In recent years, efforts have extended RG to complex networks, which challenge traditional assumptions. This Technical Review covers key approaches and open challenges.\",\"PeriodicalId\":19024,\"journal\":{\"name\":\"Nature Reviews Physics\",\"volume\":\"7 4\",\"pages\":\"203-219\"},\"PeriodicalIF\":44.8000,\"publicationDate\":\"2025-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nature Reviews Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.nature.com/articles/s42254-025-00817-5\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nature Reviews Physics","FirstCategoryId":"101","ListUrlMain":"https://www.nature.com/articles/s42254-025-00817-5","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, APPLIED","Score":null,"Total":0}
The renormalization group (RG) is a powerful theoretical framework. It is used on systems with many degrees of freedom to transform the description of their configurations, along with the associated model parameters and coupling constants, across different levels of resolution. The RG also provides a way to identify critical points of phase transitions and study the system’s behaviour around them. In traditional physical applications, the RG largely builds on the notions of homogeneity, symmetry, geometry and locality to define metric distances, scale transformations and self-similar coarse-graining schemes. More recently, efforts have been made to extend RG concepts to complex networks. However, in such systems, explicit geometric coordinates do not necessarily exist, different nodes and subgraphs can have different statistical properties, and homogeneous lattice-like symmetries are absent — all features that make it complicated to define consistent renormalization procedures. In this Technical Review, we discuss the main approaches, important advances, and the remaining open challenges for network renormalization. The renormalization group (RG) is a theoretical framework to transform systems across scales and identify critical points of phase transitions. In recent years, efforts have extended RG to complex networks, which challenge traditional assumptions. This Technical Review covers key approaches and open challenges.
期刊介绍:
Nature Reviews Physics is an online-only reviews journal, part of the Nature Reviews portfolio of journals. It publishes high-quality technical reference, review, and commentary articles in all areas of fundamental and applied physics. The journal offers a range of content types, including Reviews, Perspectives, Roadmaps, Technical Reviews, Expert Recommendations, Comments, Editorials, Research Highlights, Features, and News & Views, which cover significant advances in the field and topical issues. Nature Reviews Physics is published monthly from January 2019 and does not have external, academic editors. Instead, all editorial decisions are made by a dedicated team of full-time professional editors.