Criticality governed by the stable renormalization fixed point of the Ising model in the hierarchical small-world network

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 86, Issue 3, 2012, Pages

  Nogawa, Tomoaki ^a   Hasegawa, Takehisa ^a   Nemoto, Koji ^b  

^a TOHOKU UNIVERSITY   (Japan)

^b HOKKAIDO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

COUPLING STRENGTHS; FIXED POINTS; ORDERED PHASE; RENORMALIZATION; RENORMALIZATION GROUP ANALYSIS; SMALL WORLD NETWORKS; TRANSITION POINT; WEAK STABILITY;

ISING MODEL; STATISTICAL MECHANICS; TRANSITION FLOW;

CRITICALITY (NUCLEAR FISSION);

EID: 84866379231     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.86.030102     Document Type: Article

References (19)

1. S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.1275 80, 1275 (2008).
2. H. Shima and Y. Sakaniwa, J. Stat. Mech. 1742-5468 10.1088/1742-5468/ 2006/08/P08017 (2006) P08017.
3. M. Hinczewski and A. N. Berker, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.73.066126 73, 066126 (2006). (Pubitemid 43974164)
4. A. N. Berker, M. Hinczewski, and R. R. Netz, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.041118 80, 041118 (2009).
5. T. Nogawa and T. Hasegawa, J. Phys. A 1751-8113 10.1088/1751-8113/42/14/ 145001 42, 145001 (2009).
6. V. L. Berezinskii, Sov. Phys. JETP 34, 610 (1972).
7. J. M. Kosterlitz and D. J. Thouless, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/6/7/010 6, 1181 (1973).
8. It is better to consider local susceptibility when the system is inhomogeneous (nontransitive).
9. T. Nogawa and T. Hasegawa, J. Phys. A 1539-3755 10.1088/1751-8113/42/47/ 478002 42, 478002 (2009).
10. S. K. Baek, P. Minnhagen, and B. J. Kim, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.011124 79, 011124 (2009).
11. T. Hasegawa, M. Sato, and K. Nemoto, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.046101 82, 046101 (2010).
12. S. Boettcher, V. Singh, and R. M. Ziff, Nat. Commun. 2041-1723 10.1038/ncomms1774 3, 787 (2012).
13. T. Hasegawa and K. Nemoto, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.051105 81, 051105 (2010).
14. P. W. Kasteleyn and C. M. Fortuin, J. Phys. Soc. Jpn. 26, 11 (1969).
15. C. M. Fortuin and P. W. Kasteleyn, Physica PHYSAG 0031-8914 10.1016/0031-8914(72)90045-6 57, 536 (1972).
16. T. Nogawa, T. Hasegawa, and K. Nemoto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.108.255703 108, 255703 (2012).
17. P. L. Krapivsky and B. Derrida, Phys. A PHYADX 0378-4371 10.1016/j.physa.2004.05.020 340, 714 (2004).
18. S. Boettcher and C. T. Brunson, Phys. Rev. E 10.1103/PhysRevE.83.021103 83, 021103 (2011).
19. M. Bauer, S. Coulomb, and S. N. Dorogovtsev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.200602 94, 200602 (2005). (Pubitemid 43272577)