Replica-symmetry-breaking transitions and off-equilibrium dynamics

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

Volumn 88, Issue 3, 2013, Pages

  Rizzo, Tommaso ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL STUDIES; DYNAMICAL BEHAVIORS; DYNAMICAL TRANSITION; GLASSY SYSTEMS; NUMERICAL SOLUTION; P-SPIN MODELS; QUALITATIVE CHANGES; SYSTEM COMPLEXITY;

DYNAMICAL SYSTEMS;

DYNAMICS;

EID: 84885126722     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.88.032135     Document Type: Article

References (40)

1. T. R. Kirkpatrick and D. Thirumalai, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.36.5388 36, 5388 (1987).
2. T. R. Kirkpatrick and D. Thirumalai, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/22/5/003 22, L149 (1989).
3. A. Crisanti and H. J. Sommers, Z. Phys. B ZPCMDN 0722-3277 10.1007/BF01309287 87, 341 (1992).
4. A. Crisanti, H. Horner, and H. J. Sommers, Z. Phys. B ZPCMDN 0722-3277 10.1007/BF01312184 92, 257 (1993).
5. L. F. Cugliandolo and J. Kurchan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.173 71, 173 (1993).
6. R. Monasson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75. 2847 75, 2847 (1995).
7. S. Franz and G. Parisi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.2486 79, 2486 (1997).
8. W. Götze, Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory (Oxford University Press, Oxford, U.K., 2009).
9. G. Parisi and T. Rizzo, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.87.012101 87, 012101 (2013).
10. J. R. L. de Almeida and D. J. Thouless, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/11/5/028 11, 983 (1978).
11. E. Marinari, G. Parisi, and F. Ritort, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/27/23/011 27, 7647 (1994).
12. A. Montanari and F. Ricci-Tersenghi, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2003-00174-7 33, 339 (2003). (Pubitemid 41201070)
13. A. Crisanti, L. Leuzzi, and T. Rizzo, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.71.094202 71, 094202 (2005). (Pubitemid 40781354)
14. Y. Tonosaki, K. Takeda, and Y. Kabashima, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.75.094405 75, 094405 (2007).
15. E. Gardner, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(85)90374-8 257, 747 (1985).
16. L. Cugliandolo and J. Kurchan, Philos. Mag. B 1364-2812 10.1080/01418639508238541 71, 501 (1995).
17. S. Franz, G. Parisi, F. Ricci-Tersenghi, and T. Rizzo, Eur. Phys. J. E. EPJSFH 1292-8941 10.1140/epje/i2011-11102-0 34, 102 (2011).
18. For the sake of simplicity we are retaining only the relevant cubic terms; see Sec. for the full expression.
19. G. Parisi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.43.1754 43, 1754 (1979).
20. C. De Dominicis, T. Temesvari, and I. Kondor, J. Phys. IV 8, 6 (1998).
21. J.-P. Bouchaud, L. Cugliandolo, J. Kurchan, and M. Mezard, in Spin-Glasses and Random Fields, edited by, A. P. Young, (World Scientific, Singapore, 1998).
22. L. F. Cugliandolo and P. Le Doussal, Phys. Rev. E 1063-651X 10.1103/PhysRevE.53.1525 53, 1525 (1996).
23. F. Caltagirone, G. Parisi, and T. Rizzo, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.87.032134 87, 032134 (2013).
24. W. Götze and L. Sjögren, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/1/26/015 1, 4203 (1989).
25. S. Franz, E. Marinari, and G. Parisi, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/28/19/001 28, 5437 (1995).
26. B. Kim and A. Latz, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2001- 00202-4 53, 660 (2001).
27. A. Andreanov and A. Lefevre, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2006-10352-9 76, 919 (2006). (Pubitemid 44877375)
28. A. Montanari and F. Ricci-Tersenghi, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.70.134406 70, 134406 (2004). (Pubitemid 40018927)
29. D. J. Gross, I. Kanter, and H. Sompolinsky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.55.304 55, 304 (1985).
30. T. Temesvari, C. De Dominicis, and I. R. Pimentel, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e20020041 25, 361 (2002).
31. G. Parisi, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/13/5/047 13, 1887 (1980).
32. T. R. Kirkpatrick and D. Thirumalai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.58.2091 58, 2091 (1987).
33. U. Ferrari, L. Leuzzi, G. Parisi, and T. Rizzo, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.014204 86, 014204 (2012).
34. H. J. Sommers and W. Dupont, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/17/32/012 17, 5785 (1984).
35. H.-J. Sommers, J. Phys. (France) Lett. JPSLBO 0302-072X 10.1051/jphyslet:019850046017077900 46, L779 (1985).
36. A. Crisanti and T. Rizzo, Phys. Rev. E 1063-651X 10.1103/PhysRevE.65. 046137 65, 046137 (2002). (Pubitemid 40618938)
37. J. Kurchan, G. Parisi, and F. Zamponi, J. Stat. Mech.: Theory Exp. 10.1088/1742-5468/2012/10/P10012 (2012) P10012;
38. J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, arXiv:1303.1028 [J. Phys. Chem. B (to be published)]; (private communication).
39. S. Okamura and H. Yoshino, arXiv:1306.2777.
40. A. Crisanti and L. Leuzzi, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.76.184417 76, 184417 (2007).