Finite-size scaling of the de almeida-thouless instability in random sparse networks

Physical Review B - Condensed Matter and Materials Physics

Volumn 81, Issue 17, 2010, Pages

  Takahashi, Hisanao ^a   Ricci Tersenghi, Federico ^b   Kabashima, Yoshiyuki ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77955465333     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.174407     Document Type: Article

References (29)

1. G. Parisi, Phys. Rev. Lett. 43, 1754 (1979). 10.1103/PhysRevLett.43.1754
2. D. J. Thouless, P. W. Anderson, and R. G. Palmer, Philos. Mag. 35, 593 (1977). 10.1080/14786437708235992
3. M. Mézard, G. Parisi, and M. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
4. M. Talagrand, Spin Glasses: A Challenge for Mathematicians: Cavity and Mean Field Models (Springer, Berlin, 2003).
5. F. Guerra and F. L. Toninelli, Commun. Math. Phys. 230, 71 (2002). 10.1007/s00220-002-0699-y
6. P. Contucci, C. Giardinà, C. Giberti, G. Parisi, and C. Vernia, Phys. Rev. Lett. 99, 057206 (2007) 10.1103/PhysRevLett.99.057206
7. T. Jörg and F. Krzåkała, Phys. Rev. Lett. 100, 159701 (2008). 10.1103/PhysRevLett.100.159701
8. J. R. L. de Almeida and D. J. Thouless, J. Phys. A 11, 983 (1978). 10.1088/0305-4470/11/5/028
9. T. Aspelmeier, A. Billoire, E. Marinari, and M. A. Moore, J. Phys. A: Math. Theor. 41, 324008 (2008). 10.1088/1751-8113/41/32/324008
10. T. Jörg, H. G. Katzgraber, and F. Krzåkała, Phys. Rev. Lett. 100, 197202 (2008). 10.1103/PhysRevLett.100.197202
11. Our working definition of χ SG differs from the standard one by a factor T 2, which is, however, irrelevant in the study of its divergence.
12. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Network of Plausible Inference (Morgan Kaufmann, San Francisco, 1988).
13. Y. Kabashima and D. Saad, Europhys. Lett. 44, 668 (1998). 10.1209/epl/i1998-00524-7
14. M. Mézard and G. Parisi, Eur. Phys. J. B 20, 217 (2001). 10.1007/PL00011099
15. O. Rivoire, G. Biroli, O. C. Martin, and M. Mézard, Eur. Phys. J. B 37, 55 (2004). 10.1140/epjb/e2004-00030-4
16. F. Krzakała, A. Montanari, F. Ricci-Tersenghi, G. Semerjian, and L. Zdeborova, Proc. Natl. Acad. Sci. U.S.A. 104, 10318 (2007). 10.1073/pnas.0703685104
17. D. J. Thouless, Phys. Rev. Lett. 56, 1082 (1986). 10.1103/PhysRevLett.56. 1082
18. M. Mézard and G. Parisi, Europhys. Lett. 3, 1067 (1987). 10.1209/0295-5075/3/10/002
19. A. Pagnani, G. Parisi, and M. Ratieville, Phys. Rev. E 68, 046706 (2003). 10.1103/PhysRevE.68.046706
20. G. Parisi and T. Rizzo, J. Phys. A: Math. Theor. 43, 045001 (2010). 10.1088/1751-8113/43/4/045001
21. R. Kühn, J. Phys. A: Math. Theor. 41, 295002 (2008). 10.1088/1751-8113/41/29/295002
22. L. de Haan and A. Ferreira, Extreme Value Theory: An Introduction (Springer, New York, 2006).
23. A. Billoire and B. Coluzzi, Phys. Rev. E 68, 026131 (2003). 10.1103/PhysRevE.68.026131
24. A. Billoire and B. Coluzzi, Phys. Rev. E 67, 036108 (2003). 10.1103/PhysRevE.67.036108
25. K. Hukushima and K. Nemoto, J. Phys. Soc. Jpn. 65, 1604 (1996). 10.1143/JPSJ.65.1604
26. U. H. E. Hansmann, Chem. Phys. Lett. 281, 140 (1997). 10.1016/S0009-2614(97)01198-6
27. H. G. Katzgraber, D. Larson, and A. P. Young, Phys. Rev. Lett. 102, 177205 (2009). 10.1103/PhysRevLett.102.177205
28. L. Leuzzi, G. Parisi, F. Ricci-Tersenghi, and J. J. Ruiz-Lorenzo, Phys. Rev. Lett. 103, 267201 (2009). 10.1103/PhysRevLett.103.267201
29. C. A. Tracy and H. Widom, Phys. Lett. B 305, 115 (1993). 10.1016/0370-2693(93)91114-3