K-core attack, equilibrium K-core, and kinetically constrained spin system

doi:10.1088/1674-1056/ad4329

中国物理B ›› 2024, Vol. 33 ›› Issue (6): 66402-066402.doi: 10.1088/1674-1056/ad4329

所属专题： SPECIAL TOPIC — States and new effects in nonequilibrium

K-core attack, equilibrium K-core, and kinetically constrained spin system

Hai-Jun Zhou(周海军)^1,2,3,†

1 Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China;
2 MinJiang Collaborative Center for Theoretical Physics, MinJiang University, Fuzhou 350108, China;
3 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

收稿日期:2024-03-14 修回日期:2024-04-14 接受日期:2024-04-25 出版日期:2024-06-18 发布日期:2024-06-18
通讯作者: Hai-Jun Zhou E-mail:zhouhj@itp.ac.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12247104 and 12047503).

K-core attack, equilibrium K-core, and kinetically constrained spin system

Hai-Jun Zhou(周海军)^1,2,3,†

1 Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China;
2 MinJiang Collaborative Center for Theoretical Physics, MinJiang University, Fuzhou 350108, China;
3 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2024-03-14 Revised:2024-04-14 Accepted:2024-04-25 Online:2024-06-18 Published:2024-06-18
Contact: Hai-Jun Zhou E-mail:zhouhj@itp.ac.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12247104 and 12047503).

摘要/Abstract

摘要： 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.

关键词: Fredrickson-Andersen model, $K$-core attack, spin glass, jamming

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.

Key words: Fredrickson-Andersen model, $K$-core attack, spin glass, jamming

中图分类号: (Theory and modeling of the glass transition)

64.70.Q-

05.70.Fh (Phase transitions: general studies) 75.10.Nr (Spin-glass and other random models) 89.75.Fb (Structures and organization in complex systems)

Hai-Jun Zhou(周海军). K-core attack, equilibrium K-core, and kinetically constrained spin system[J]. 中国物理B, 2024, 33(6): 66402-066402.

Hai-Jun Zhou(周海军). K-core attack, equilibrium K-core, and kinetically constrained spin system[J]. Chin. Phys. B, 2024, 33(6): 66402-066402.

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K-core attack, equilibrium K-core, and kinetically constrained spin system

K-core attack, equilibrium K-core, and kinetically constrained spin system

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