Metastable states and T=0 hysteresis in the random-field Ising model on random graphs

European Physical Journal B

Volumn 44, Issue 3, 2005, Pages 327-343

  Detcheverry, F ^a   Rosinberg, M L ^a   Tarjus, G ^a  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ANNEALING; COMPUTATIONAL COMPLEXITY; CRYSTAL LATTICES; FERROMAGNETISM; GRAPH THEORY; HYSTERESIS; MAGNETIC FIELDS; MAGNETIZATION; MATHEMATICAL MODELS; QUENCHING; SPIN GLASS; STATISTICAL METHODS;

BARKHAUSEN AND RELATED EFFECTS; LATTICE THEORY AND STATISTICS; MAGNETIZATION CURVES; SPIN-GLASS AND OTHER RANDOM MODELS;

RANDOM PROCESSES;

EID: 18244388952     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1140/epjb/e2005-00132-5     Document Type: Article

References (29)

1. J.P. Sethna, K. Dahmen, S. Kartha, J.A. Krumhansl, B.W. Roberts, J.D. Shore, Phys. Rev. Lett. 70, 3347 (1993)
2. K. Dahmen, J.P. Sethna, Phys. Rev. B 53, 14872 (1996);
3. O. Perkovic, K. Dahnen, J.P. Sethna, Phys. Rev. B 50, 6106 (1999)
4. P. Shukla, Physica A 233, 235 (1996)
5. D. Dhar, P. Shukla, J.P. Sethna, J. Phys. A 30, 5259 (1997)
6. A. Berger, A. Inomata, J.S. Jiang, J.E. Pearson, S.D. Bader, Phys. Rev. Lett. 85, 4176 (2000)
7. J. Marcos, E. Vives, Ll. Mañosa, M. Acet, E. Duman, M. Morin, V. Novak, A. Planes, Phys. Rev. B 67, 224406 (2003)
8. F. Detcheverry, E. Kierlik, M.L. Rosinberg, G. Tarjus, Phys. Rev. E 68, 061504 (2003);
9. F. Detcheverry, E. Kierlik, M.L. Rosinberg, G. Tarjus, Langmuir 20, 8006 (2004)
10. D.J. Tulimieri, J. Yoon, M.H.W. Chan, Phys. Rev. Lett. 82, 121 (1999)
11. In this work, we study the 1-spin-flip stable states whose energy cannot be lowered by the flip of any single spin. The corresponding dynamics consists in aligning each spin with its local field. Generalization to 2-spin-flip stable states and associated dynamics is considered in E. Vives, M.L. Rosinberg, G. Tarjus, Phys. Rev. B (in press), preprint cond-mat/0411330 (2004)
12. F. Pazmandi, G. Zarand, G. Zimanyi, Phys. Rev. Lett. 83, 1034 (1999)
13. A.A. Likhachev, preprint cond-mat/0007504 (2000)
14. F. Colaiori, A. Gabrielli, S. Zapperi, Phys. Rev. B 65, 224404 (2002)
15. M. Mezard, G. Parisi, Eur. Phys. J. B 20, 217 (2001)
16. A. Lefèvre, D.S. Dean, Eur. Phys. J. B 21, 121 (2001)
17. J. Berg, M. Sellito, Phys. Rev. E 65, 016115 (2001)
18. A. Pagnani, G. Parisi, M. Ratiéville, Phys. Rev. E 67, 026116 (2003)
19. D.S. Dean, Eur. Phys. J. B 15, 493 (2000)
20. S. Masui, A.E. Jacobs, C. Wicentowich, B.W. Southern, J. Phys. A 26, 25 (1993)
21. More precisely, we expect the complexities, as defined below, to be equal. It was checked numerically in reference [4] that the hysteresis loops are identical in the thermodynamic limit
22. L. Viana, A.J. Bray, J. Phys. C. 18, 3037 (1985)
23. V. Basso, A. Magni, private communication
24. T. Schneider, E. Pytte, Phys. Rev. B 15, 1519 (1977)
25. S. Franz, private communication
26. i = ±1 with probability 1/2); this latter process corresponds to an instantaneous "quench" of the system from an infinite temperature to T = 0. This result (if confirmed) implies that the basins of attraction of the metastable states do not have the same size under the one-spin-flip dynamics.
27. R.O. Sokolovskii, M.E. Cates, T.G. Sokolovska, Phys. Rev. E 68, 026124 (2003)
28. V. Basso, A. Magni, Physica B 343, 275 (2004)
29. Note that the reverse (inner) trajectories which bound the two domains of existence of the H-states start from the last available states on the convex parts of the major loop (spinodals) and meet the concave, inaccessible parts of that loop at the two singular points with an infinite slope. The fields at the starting and meeting points are separated by 2J, which shows that the proof given by P. Shukla in Phys. Rev. E 63, 27102 (2001) is applicable even in the case of a discontinuous hysteresis loop