Criticality and scaling behavior of percolation with multiple giant clusters under an Achlioptas process

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

Volumn 88, Issue 6, 2013, Pages

  Zhang, Yang ^a   Wei, Wei ^a   Guo, Binghui ^a   Zhang, Renquan ^a   Zheng, Zhiming ^a  

^a BEIHANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLETE SCALING THEORIES; CRITICAL EXPONENT; CRITICAL PHENOMENON; FINITE-SIZE SCALING ANALYSIS; PARAMETER INTERVALS; PERCOLATION MODELS; PERCOLATION TRANSITION; SUPER-CRITICAL REGIONS;

CRITICALITY (NUCLEAR FISSION); MONTE CARLO METHODS; PERCOLATION (SOLID STATE);

SOLVENTS;

EID: 84890533557     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.88.062103     Document Type: Article

References (31)

1. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor & Francis, London, 1994).
2. M. Sahimi, Applications of Percolation Theory (Taylor & Francis, London, 1994).
3. B. Bollobás, Random Graphs, 2nd ed. (Cambridge University Press, Cambridge, UK, 2001).
4. D. Achlioptas, R. M. D'Souza, and J. Spencer, Science SCIEAS 0036-8075 10.1126/science.1167782 323, 1453 (2009).
5. R. A. da Costa, S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.255701 105, 255701 (2010).
6. P. Grassberger, C. Christensen, G. Bizhani, S.-W. Son, and M. Paczuski, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.225701 106, 225701 (2011).
7. H. K. Lee, B. J. Kim, and H. Park, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.84.020101 84, 020101 (R) (2011).
8. L. Tian and D.-N. Shi, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2011.11.039 376, 286 (2012).
9. O. Riordan and L. Warnke, Science SCIEAS 0036-8075 10.1126/science. 1206241 333, 322 (2011).
10. R. M. Ziff, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.051105 82, 051105 (2010).
11. O. Riordan and L. Warnke, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.86.011129 86, 011129 (2012).
12. J. Nagler, T. Tiessen, and H. W. Gutch, Phys. Rev. X 2160-3308 10.1103/PhysRevX.2.031009 2, 031009 (2012).
13. T. Bohman, A. Frieze, and N. C. Wormald, Random Struct. Algor. 1042-9832 10.1002/rsa.20038 25, 432 (2004).
14. W. Chen and R. M. D'Souza, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.115701 106, 115701 (2011).
15. K. J. Schrenk, A. Felder, S. Deflorin, N. A. M. Araújo, R. M. D'Souza, and H. J. Herrmann, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85. 031103 85, 031103 (2012).
16. Y. Zhang, W. Wei, B. Guo, R. Zhang, and Z. Zheng, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.86.051103 86, 051103 (2012).
17. O. Riordan and L. Warnke, Ann. Appl. Probab. 1050-5164 10.1214/11-AAP798 22, 1450 (2012).
18. R. M. D'Souza and M. Mitzenmacher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.195702 104, 195702 (2010).
19. E. Ben-Naim and P. L. Krapivsky, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/23/L01 38, L417 (2005).
20. W. Chen, Z. Zheng, and R. M. D'Souza, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/100/66006 100, 66006 (2012).
21. D. P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge, UK, 2000).
22. Finite Size Scaling and Numerical Simulation of Statistical Systems, edited by V. Privman (World Scientific, Singapore, 1990).
23. J. Fan, M. Liu, L. Li, and X. Chen, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.061110 85, 061110 (2012).
24. W. Chen, J. Nagler, X. Cheng, X. Jin, H. Shen, Z. Zheng, and R. M. D'Souza, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.87.052130 87, 052130 (2013).
25. M. E. Fisher, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.70.653 70, 653 (1998).
26. H. E. Stanley, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.71. S358 71, S358 (1999).
27. M. X. Liu, J. F. Fan, L. S. Li, and X. S. Chen, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2012-20872-1 85, 132 (2012).
28. E. J. Friedman and A. S. Landsberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.255701 103, 255701 (2009).
29. K. Christensen and N. R. Moloney, Complexity and Criticality (Imperial College Press, London, 2005).
30. S. D. S. Reis, A. A. Moreira, and J. S. Andrade, Jr., Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.041112 85, 041112 (2012).
31. P.-S. Shim, H. K. Lee, and J. D. Noh, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.86.031113 86, 031113 (2012).