{"title":"K-core attack, equilibrium K-core, and kinetically constrained spin system","authors":"Hai-Jun Zhou","doi":"10.1088/1674-1056/ad4329","DOIUrl":null,"url":null,"abstract":"\n Kinetically constrained spin systems are toy models of supercooled liquids and amorphous solids. In this Perspective, we revisit the prototypical Fredrickson-Andersen (FA) kinetically constrained model from the viewpoint of K-core combinatorial optimization. Each kinetic cluster of the FA system, containing all the mutually visitable microscopic occupation configurations, is exactly the solution space of a specific instance of the K-core attack problem. The whole set of different jammed occupation patterns of the FA system is the configuration space of an equilibrium K-core problem. Based on recent theoretical results achieved on the K-core attack and equilibrium K-core problems, we discuss the thermodynamic spin glass phase transitions and the maximum occupation density of the fully unfrozen FA kinetic cluster, and the minimum occupation density and extreme vulnerability of the partially frozen (jammed) kinetic clusters. The equivalence between K-core attack and the fully unfrozen FA kinetic cluster also implies a new way of sampling K-core attack solutions.","PeriodicalId":10253,"journal":{"name":"Chinese Physics B","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chinese Physics B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1674-1056/ad4329","RegionNum":4,"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
Kinetically constrained spin systems are toy models of supercooled liquids and amorphous solids. In this Perspective, we revisit the prototypical Fredrickson-Andersen (FA) kinetically constrained model from the viewpoint of K-core combinatorial optimization. Each kinetic cluster of the FA system, containing all the mutually visitable microscopic occupation configurations, is exactly the solution space of a specific instance of the K-core attack problem. The whole set of different jammed occupation patterns of the FA system is the configuration space of an equilibrium K-core problem. Based on recent theoretical results achieved on the K-core attack and equilibrium K-core problems, we discuss the thermodynamic spin glass phase transitions and the maximum occupation density of the fully unfrozen FA kinetic cluster, and the minimum occupation density and extreme vulnerability of the partially frozen (jammed) kinetic clusters. The equivalence between K-core attack and the fully unfrozen FA kinetic cluster also implies a new way of sampling K-core attack solutions.
动力学约束自旋系统是过冷液体和无定形固体的玩具模型。在本《视角》中,我们从 K 核组合优化的角度重新审视了原型弗雷德里克森-安德森(Fredrickson-Andersen,FA)动力学约束模型。FA 系统的每个动力学簇包含所有可相互访问的微观占位配置,正是 K 核攻击问题特定实例的解空间。整个 FA 系统的不同干扰占据模式集合就是均衡 K 核问题的配置空间。基于最近在 K 核攻击和平衡 K 核问题上取得的理论成果,我们讨论了完全解冻的 FA 动力簇的热力学自旋玻璃相变和最大占据密度,以及部分冻结(卡住)的动力簇的最小占据密度和极端脆弱性。K 核攻击与完全解冻的 FA 动力簇之间的等价关系也意味着一种新的 K 核攻击解决方案采样方法。
期刊介绍:
Chinese Physics B is an international journal covering the latest developments and achievements in all branches of physics worldwide (with the exception of nuclear physics and physics of elementary particles and fields, which is covered by Chinese Physics C). It publishes original research papers and rapid communications reflecting creative and innovative achievements across the field of physics, as well as review articles covering important accomplishments in the frontiers of physics.
Subject coverage includes:
Condensed matter physics and the physics of materials
Atomic, molecular and optical physics
Statistical, nonlinear and soft matter physics
Plasma physics
Interdisciplinary physics.