Rounding of first-order phase transitions and optimal cooperation in scale-free networks

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

Volumn 76, Issue 4, 2007, Pages

  Karsai, M ^a,b   D'Auriac, J Ch Anglès ^b   Igloi F ^a,c  

^a UNIVERSITY OF SZEGED   (Hungary)

^b LABORATOIRE DE CRISTALLOGRAPHIE   (France)

^c WIGNER RESEARCH CENTRE FOR PHYSICS   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTER ANALYSIS; FERROMAGNETIC MATERIALS; MAGNETIZATION; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; OPTIMIZATION; PROBLEM SOLVING;

FIRST ORDER PHASE TRANSITIONS; HOMOGENEOUS MODELS; OPTIMAL COOPERATION PROBLEMS; SHIFT EXPONENTS;

PHASE TRANSITIONS;

EID: 35248897198     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.041107     Document Type: Article

References (54)

1. R. Albert and A. L. Barabási, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.47 74, 47 (2002).
2. S. N. Dorogovtsev and J. F. F. Mendes, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730110112519 51, 1079 (2002).
3. S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, Oxford, 2003).
4. M. E. J. Newman, SIAM Rev. SIREAD 0036-1445 10.1137/S003614450342480 45, 167 (2003).
5. B. Bollobás, Random Graphs (Academic Press, London, 1985).
6. D. J. Watts and S. H. Strogatz, Nature (London) NATUAS 0028-0836 10.1038/30918 393, 440 (1998).
7. A. L. Barabási and R. Albert, Science SCIEAS 0036-8075 10.1126/science.286.5439.509 286, 509 (1999).
8. R. Pastor-Satorras and A. Vespignani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.3200 86, 3200 (2001)
9. R. Pastor-Satorras and A. Vespignani, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.066117 63, 066117 (2001).
10. M. E. J. Newman, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.016128 66, 016128 (2002).
11. Z. Dezso and A.-L. Barabási, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.055103 65, 055103 (R) (2002).
12. D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.5468 85, 5468 (2000)
13. R. Cohen, D. ben-Avraham, and S. Havlin, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.036113 66, 036113 (2002).
14. J.-D. Noh and H. Rieger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.118701 92, 118701 (2004).
15. M. Karsai, R. Juhász, and F. Iglói, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.036116 73, 036116 (2006).
16. J.-D. Noh, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.056123 72, 056123 (2005).
17. A. Aleksiejuk, J. A. Holyst, and D. Stauffer, Physica A PHYADX 0378-4371 10.1016/S0378-4371(02)00740-9 310, 260 (2002).
18. M. Leone, A. Vazquez, A. Vespignani, and R. Zecchina, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2002-00220-0 28, 191 (2002)
19. S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.016104 66, 016104 (2002)
20. G. Bianconi, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(02)01232-X 303, 166 (2002).
21. F. Iglói and L. Turban, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.036140 66, 036140 (2002).
22. S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2004-00019-y 38, 177 (2004).
23. C. V. Giuraniuc, J. P. L. Hatchett, J. O. Indekeu, M. Leone, I. Perez Castillo, B. Van Schaeybroeck, and C. Vanderzande, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.098701 95, 098701 (2005)
24. C. V. Giuraniuc, J. P. L. Hatchett, J. O. Indekeu, M. Leone, I. Perez Castillo, B. Van Schaeybroeck, and C. Vanderzande, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.74.036108 74, 036108 (2006).
25. M. A. Sumour, A. H. El-Astal, F. W. S. Lima, M. M. Shabat, and H. M. Khalil, Int. J. Mod. Phys. C IJMPEO 0129-1831 10.1142/S0129183107010346 18, 53 (2007).
26. M. Aizenman and J. Wehr, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62.2503 62, 2503 (1989)
27. M. Aizenman and J. Wehr, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.1311 64, 1311 (E) (1990);
28. K. Hui and A. N. Berker, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62.2507 62, 2507 (1989).
29. K. Uzelac, A. Hasmy, and R. Jullien, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.422 74, 422 (1995).
30. H. G. Ballesteros, L. A. Fernández, V. Martìn-Mayor, A. Muñoz Sudupe, G. Parisi, and J. J. Ruiz-Lorenzo, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.61.3215 61, 3215 (2000).
31. C. Chatelain, B. Berche, W. Janke, and P.-E. Berche, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.036120 64, 036120 (2001)
32. W. Janke, P.-E. Berche, C. Chatelain, and B. Berche, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2005.05.003 719, 275 (2005).
33. M.-T. Mercaldo, J-Ch. Anglés d'Auriac, and F. Iglói, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2005-10042-2 70, 733 (2005).
34. M.-T. Mercaldo, J-Ch. Anglés d'Auriac, and F. Iglói, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.026126 73, 026126 (2006).
35. J.-Ch. Anglès d'Auriac, F. Iglói, M. Preissmann, and A. Sebö, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/33/301 35, 6973 (2002)
36. J.-Ch. Anglès d'Auriac, in New Optimization Algorithms in Physics, edited by, A. K. Hartmann, and, H. Rieger, (Wiley-VCH, Berlin, 2004).
37. R. Juhász, H. Rieger, and F. Iglói, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.056122 64, 056122 (2001).
38. P. W. Kasteleyn and C. M. Fortuin, J. Phys. Soc. Jpn. (Suppl.) 46, 11 (1969). 0031-9015
39. F. Y. Wu, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.54.235 54, 235 (1982).
40. M.-T. Mercaldo, J-Ch. Anglés d'Auriac, and F. Iglói, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.056112 69, 056112 (2004).
41. M. Grötschel, L. Lovász, and A. Schrijver, Combinatorica COMBDI 0209-9683 10.1007/BF02579273 1, 169 (1981).
42. J.-Ch. Anglès d'Auriac and F. Iglói, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.190601 90, 190601 (2003).
43. P. Erdos and A. Rényi, Publ. Math. (Debrecen) PUMAAR 0033-3883 6, 290 (1959)
44. P. Erdos and A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960).
45. C. Monthus and T. Garel, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2005-00417-7 48, 393 (2005).
46. S. Wiseman and E. Domany, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.52.3469 52, 3469 (1995).
47. A. Aharony and A. B. Harris, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.3700 77, 3700 (1996).
48. F. Pázmándi, R. T. Scalettar, and G. T. Zimányi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.5130 79, 5130 (1997).
49. S. Wiseman and E. Domany, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.22 81, 22 (1998)
50. S. Wiseman and E. Domany, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.58.2938 58, 2938 (1998).
51. A. Aharony, A. B. Harris, and S. Wiseman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.252 81, 252 (1998).
52. J. T. Chayes, L. Chayes, D. S. Fisher, and T. Spencer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.57.2999 57, 2999 (1986).
53. D. S. Fisher, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.51.6411 51, 6411 (1995).
54. F. Iglói, Y.-C. Lin, H. Rieger, and C. Monthus, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.064421 76, 064421 (2007).