Lyapunov exponents as a dynamical indicator of a phase transition

Europhysics Letters

Volumn 55, Issue 2, 2001, Pages 164-170

  Barre J ^a   Dauxois, T ^a  

^a UNIVERSITÉ DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035796129     PISSN: 02955075     EISSN: None     Source Type: Journal    
DOI: 10.1209/epl/i2001-00396-3     Document Type: Article

References (23)

1. MANNEVILLE P., Structures Dissipatives, Chaos et Turbulence (Aléa Saclay) 1991.
2. LICHTENBERG A. J. and LIEBERMAN M. A., Regular and Chaotic Dynamics (Springer, Berlin) 1992.
3. CASETTI L., LIVI R. and PETTINI M., Phys. Rev. Lett., 74 (1995) 375.
4. CONSTANTOUDIS V. and THEODORAKOPOULOS N., Phys. Rev. E, 55 (1997) 7612.
5. LATORA V., RAPISARDA A. and RUFFO S., Physica D, 131 (1999) 38.
6. FIRPO M. C., Phys. Rev. E, 57 (1998) 6599.
7. CASETTI L., PETTINI M. and COHEN E. G. D., Phys. Rep., 337 (2000) 237.
8. COCCO S. and MONASSON R., Phys. Rev. Lett., 83 (1999) 5178.
9. CAUSO M. S., COLUZZI B. and GRASSBERGER P., Phys. Rev. E, 62 (2000) 3958.
10. KAFRI Y., MUKAMEL D. and PELLITI L., Phys. Rev. Lett., 85 (2000) 4988.
11. GAREL T., MONTHUS C. and ORLAND H., cond-mat/0101058.
12. THEODORAKOPOULOS N., DAUXOIS T. and PEYRARD M., Phys. Rev. Lett., 85 (2000) 6.
13. LEBOWITZ J. L., PERCUS J. K. and VERLET L., Phys. Rev., 153 (1967) 250.
14. -1 and m = 300 a.m.u.
15. BENETTIN G. et al., Meccanica, 9 (1980) 21.
16. CAIANI L. et al., Phys. Rev. E, 57 (1998) 3886. 7
17. MAC KAY R. S. and AUBRY S., Nonlinearity, 7 (1994) 1623.
18. Results reported in [12] clearly shows the behavior of a first-order phase transition with an unusual diverging correlation length. However, it is likely that the order of the transition would be second order in the critical region which is extremely thin and unreachable numerically. See ZIA R. K. P., LIPOWSKY R. and KROLL D. M., Am. J. Phys., 56 (1988) 160 or THEODORAKOPOULOS N., unpublished (2000). However, as the width of this critical region could be decreased only by decreasing the ratio α/α, this phase transition will be considered as first-order-like.
19. Results reported in [12] clearly shows the behavior of a first-order phase transition with an unusual diverging correlation length. However, it is likely that the order of the transition would be second order in the critical region which is extremely thin and unreachable numerically. See ZIA R. K. P., LIPOWSKY R. and KROLL D. M., Am. J. Phys., 56 (1988) 160 or THEODORAKOPOULOS N., unpublished (2000). However, as the width of this critical region could be decreased only by decreasing the ratio α/α, this phase transition will be considered as first-order-like.
20. MEHRA V. and RAMASWMY R., Phys. Rev. E, 56 (1997) 2508.
21. 1 being more localized in space at high energy. See DAUXOIS T., RUEFO S. and A. TORCINI, Phys. Rev. E, 56 (1997) R6229.
22. PIKOVSKY A. and POLITI A., Nonlinearity, 11 (1999) 1049.
23. KOCKELKOREN J. and CHATÉ H., unpublished (2000).