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 — Heat conduction and its related interdisciplinary areas

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.

参考文献

[1] He D R, Liu Z H and Wang B H 2009 Complex Systems and Complex Networks (Beijing: Higher Education Press)
[2] LI J, Wang B H, Wang W X and Zhou T 2008 Chin. Phys. Lett. 25 4177
[3] Kong Y X, Shi G Y, Wu R J and Zhang Y C 2019 Phys. Rep. 832 1
[4] De Gregorio P, Lawlor A and Dawson K A 2016 Encyclopedia of Complexity and Systems Science (New York: Springer) pp. 1-26
[5] Chalupa J, Leath P L and Reich G R 1979 J. Phys. C: Solid State Phys. 12 L31
[6] Seidman S B 1983 Soc. Networks 5 269
[7] Branco N S 1993 J. Stat. Phys. 70 1035
[8] Ritort F and Sollich P 2003 Adv. Phys. 52 219
[9] Garrahan J P, Sollich P and Toninelli C 2011 Dynamical Heterogeneities in Glasses, Colloids and Granular Media (New York: Oxford University Press) pp. 341-369
[10] Jack R L 2020 Eur. Phys. J. B 93 74
[11] Fredrickson G H and Andersen H C 1984 Phys. Rev. Lett. 53 1244
[12] Tang Y, Liu J, Zhang J and Zhang P 2024 Nat. Commun. 15 1117
[13] Franz S, Gradenigo G and Spigler S 2016 Phys. Rev. E 93 032601
[14] Foini L, Krzakala F and Zamponi F 2012 J. Stat. Mech. Theory Exp. 2012 P06013
[15] Adler J 1991 Physica A 171 453
[16] Rizzo T 2019 Phys. Rev. Lett. 122 108301
[17] Perrupato G and Rizzo T 2022 arXiv:2212.05132
[cond-mat.dis-nn]
[18] Perrupato G and Rizzo T 2023 arXiv:2312.01430
[cond-mat.dis-nn]
[19] Pittel B, Spencer J and Wormald N 1996 J. Combin. Theory Ser. B 67 111
[20] Dorogovtsev S N, Goltsev A V and Mendes J F F 2006 Phys. Rev. Lett. 96 040601
[21] Zhao J H, Zhou H J and Liu Y Y 2013 Nat. Commun. 4 2412
[22] Cellai D, Lawlor A, Dawson K A and Gleeson J P 2011 Phys. Rev. Lett. 107 175703
[23] Baxter G J, Dorogovtsev S N, Goltsev A V and Mendes J F F 2011 Phys. Rev. E 83 051134
[24] Sellitto M, Biroli G and Toninelli C 2005 Europhys. Lett. 69 496
[25] Schwarz J M, Liu A J and Chayes L Q 2006 Europhys. Lett. 73 560
[26] Monone F, Burleson-Lesser K, Vinutha H A, Sastry S and Makse H A 2019 Physica A 516 172
[27] Biroli G and Mézard M 2002 Phys. Rev. Lett. 88 025501
[28] Rivoire O, Biroli G, Martin O C and Mézard M 2004 Eur. Phys. J. B 37 55
[29] Zhou H J 2022 Sci. China-Phys. Mech. Astron. 65 230511
[30] Guggiola A and Semerjian G 2015 J. Stat. Phys. 158 300
[31] Zhao J, Wu J, Chen M, Fang Z and Xu K 2015 World Wide Web 18 749
[32] Yuan X, Dai Y, Stanley H E and Havlin S 2016 Phys. Rev. E 93 062302
[33] Schmidt C, Pfister H D and Zdeborová L 2019 Phys. Rev. E 99 022310
[34] Zhou J and Zhou H J 2023 J. Stat. Phys. 190 200
[35] Fomin F V, Gaspers S, Pyatkin A V and Razgon I 2008 Algorithmica 52 293
[36] Zhou H J 2013 Eur. Phys. J. B 86 455
[37] Morone F and Makse H A 2015 Nature 524 65
[38] Mugisha S and Zhou H J 2016 Phys. Rev. E 94 012305
[39] Braunstein A, Dall’Asta L, Semerjian G and Zdeborová L 2016 Proc. Natl. Acad. Sci. USA 113 12368
[40] Zdeborova L, Zhang P and Zhou H J 2016 Sci. Rep. 6 37954
[41] Chujyo M and Hayashi Y 2021 Appl. Network Sci. 6 3
[42] Lü L, Chen D, Ren X L, Zhang Q M, Zhang Y C and Zhou T 2016 Phys. Rep. 650 1
[43] Pei S, Wang J, Morone F and Makse H A 2020 J. Complex Netw. 8 cnz029
[44] Weigt M and Hartmann A K 2001 Phys. Rev. E 63 056127
[45] Zhou H J 2003 Eur. Phys. J. B 32 265
[46] Zhao J H and Zhou H J 2014 Chin. Phys. B 23 078901
[47] Haynes T W, Hedetniemi S T and Slater P J 1998 Fundamentals of Domination in Graphs (New York: Marcel Dekker)
[48] Echenique P, Gómez-Gardeńes J, Moreno Y and V azquez A 2005 Phys. Rev. E 71 035102
[49] Zhao J H, Habibulla Y and Zhou H J 2015 J. Stat. Phys. 159 1154
[50] Mézard M, Parisi G and Zecchina R 2002 Science 297 812
[51] Mézard M and Parisi G 2001 Eur. Phys. J. B 20 217
[52] Mézard M and Parisi G 2003 J. Stat. Phys. 111 1
[53] Krzakala F, Montanari A, Ricci-Tersenghi F, Semerjian G and Zdeborová L 2007 Proc. Natl. Acad. Sci. USA 104 10318
[54] Mézard M and Montanari A 2009 Information, Physics, and Computation (New York: Oxford University Press)
[55] Zhou H J 2015 Spin Glass and Message Passing (Beijing: Science Press)
[56] Altarelli F, Braunstein A, Dall’Asta L and Zecchina R 2013 J. Stat. Mech.: Theory Exp. 2013 P09011
[57] Altarelli F, Braunstein A, Dall’Asta L and Zecchina R 2013 Phys. Rev. E 87 062115
[58] Li T, Zhang P and Zhou H J 2021 Phys. Rev. E 103 L061302
[59] Qin S M and Zhou H J 2014 Eur. Phys. J. B 87 273
[60] Bau S, Wormald N C and Zhou S 2002 Random Struct. Algorithms 21 397
[61] Mézard M and Montanari A 2006 J. Stat. Phys. 124 1317
[62] Qin S M, Zeng Y and Zhou H J 2016 Phys. Rev. E 94 022146
[63] Zhang P, Zeng Y and Zhou H J 2009 Phys. Rev. E 80 021122
[64] Urbani P, Jin Y and Yoshino H 2023 Spin Glass Theory and Far Beyond: Replica Symmetry Breaking After 40 Years (Singapore: World Scientific) pp. 219-238
[65] Liao Q, Berthier L, Zhou H J and Xu N 2023 Proc. Natl. Acad. Sci. USA 120 e2218218120
[66] Berthier L, Charbonneau P, Jin Y, Parisi G, Seoane B and Zamponi F 2016 Proc. Natl. Acad. Sci. USA 113 8397
[67] Bianconi G and Dorogovtsev S N 2024 Phys. Rev. E 109 014307
[68] Wang S N, Cheng L and Zhou H J 2020 Europhys. Lett. 132 60006
[69] Sur A, Lebowitz J L, Marro J, Kalos M H and Kirkpatrick S 1976 J. Stat. Phys. 15 345
[70] van Enter A C D 1987 J. Stat. Phys. 48 943
[71] Schonmann R H 1990 J. Stat. Phys. 58 1239
[72] Schonmann R H 1992 Ann. Probab. 20 174
[73] Lin C Y and Hu C K 1998 Phys. Rev. E 58 1521
[74] Branco N S and Silva C J 1999 Int. J. Mod. Phys. C 10 921
[75] Kurtsiefer D 2003 Int. J. Mod. Phys. C 14 529
[76] De Gregorio P, Lawlor A, Bradley P and Dawson K A 2004 Phys. Rev. Lett. 93 025501
[77] Zhu Y, Yang Z Q, Zhang X and Chen X S 2015 Commun. Theor. Phys. 64 231
[78] Xu Y Z, Yeung C H, Zhou H J and Saad D 2018 Phys. Rev. Lett. 121 210602
[79] Jin Y and Yoshino H 2021 Proc. Natl. Acad. Sci. USA 118 e2021794118
[80] Wilken S, Guerra R E, Levine D and Chaikin P M 2021 Phys. Rev. Lett. 127 038002
[81] Ozawa M, Berthier L and Coslovich D 2017 SciPost Phys. 3 027
[82] Woodcock L V 2013 Philos. Mag. 93 4159
[83] Li S X, Zhao J, Peng L P and Xie Y 2010 Chin. Sci. Bull. 55 114
[84] Jin Y and Makse H A 2010 Physica A 389 5362
[85] Pan D, Wang Y, Yoshino H, Zhang J and Jin Y 2023 Phys. Rep. 1038 1
[86] Folena G, Franz S and Ricci-Tersenghi F 2020 Phys. Rev. X 10 031045
[87] Liu J, Tong H, Nie Y and Xu N 2020 Chin. Phys. B 29 126302
[88] Chen Y, Ye Z, Wang K, Huang J, Tong H, Jin Y, Chen K, Tanaka H and Tan P 2023 Nat. Phys. 19 969

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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