Computational Complexity

2012 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Record Statistics and Dynamics

  • Paolo Sibani
  • Henrik, Jeldtoft Jensen
Reference work entry

Article Outline


Definition of the Subject


Complex Dynamics

The Distribution of Records in Stationary Time Series

Aging and Metastability

Marginal Stability

Record Statistics and Intermittency in Glassy Dynamics

Future Directions




Marginal Stability Vertical Jump Glassy System Attractor Basin Aging Dynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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The authors are indebted to P. Anderson, J. Dall, L. Oliveira and S. Boettcher. P. Sibani did part of thiswork while visiting the Cherry L. Emerson Center for Scientific Computation at Emory University.


Primary Literature

  1. 1.
    Anderson P, Jensen HJ, Oliveira LP, Sibani P (2004) Evolution in complex systems. Complexity 10:49–56MathSciNetCrossRefGoogle Scholar
  2. 2.
    Angelani L, Di Leonardo R, Parisi G, Ruocco G (2003) Topological description of the aging dynamics in simple glasses. Phys Rev Lett 87:055502CrossRefGoogle Scholar
  3. 3.
    Bak P (1997) How Nature Works. The science of self‐organized criticality. Oxford University Press, OxfordGoogle Scholar
  4. 4.
    Bak P, Tang C, Wiesenfeld K (1987) Self‐organized criticality: An explanation of 1/f noise. Phys Rev Lett 59:381–384MathSciNetCrossRefGoogle Scholar
  5. 5.
    Boettcher S, Percus A (2001) Optimization with extremal dynamics. Phys Rev Lett 86:5211–5214CrossRefGoogle Scholar
  6. 6.
    Bouchaud JP (1992) Weak ergodicity breaking and aging in disordered systems. J Phys I France 2:1705–1713CrossRefGoogle Scholar
  7. 7.
    Bray AJ, Moore MA (1987) Chaotic nature of the spin-glass phase. Phys Rev Lett 58:57–60CrossRefGoogle Scholar
  8. 8.
    Buisson L, Bellon L, Ciliberto S (2003) Intermittency in aging. J Phys Condens Matter 15:S1163CrossRefGoogle Scholar
  9. 9.
    Christensen K, di Collobiano SA, Hall M, Jensen HJ (2002) Tangled Nature: A Model of Evolutionary Ecology. J Theor Biol 216:73–84MathSciNetCrossRefGoogle Scholar
  10. 10.
    Cipelletti L, Manley S, Ball RC, Weitz DA. Universal aging features in the restructuring of fractal colloidal gels. Phys Rev Lett 84:2275–2278Google Scholar
  11. 11.
    Civale L, Marwick AD, McElfresh MW, Worthington TK, Malozemoff AP, Holtzberg FH, Thompson JR, Kirk MA (1990) Defect independence of the irreversibility line in proton‐irradiated y-ba-cu-o crystals. Phys Rev Lett 65(9):1164–1167CrossRefGoogle Scholar
  12. 12.
    Coppersmith SN, Littlewood PB (1987) Pulse‐duration memory effect and deformable charge‐density waves. Phys Rev B 36:311–317CrossRefGoogle Scholar
  13. 13.
    Cugliandolo LF, Kurchan J, Peliti L (1997) Energy flow, partial equilibration, and effective temperature in systems with slow dynamics. Phys Rev E 55:3898–3914CrossRefGoogle Scholar
  14. 14.
    Davidsen J, Grassberger P, Paczuski M (2007) Networks of recurrent events, a theory of records, and an application to finding causal signatures in seismicity. cond-mat/0701190Google Scholar
  15. 15.
    Fisher DS, Huse DA (1986) Ordered phase of short-range Ising spin‐glasses. Phys Rev Lett 56:1601–1604CrossRefGoogle Scholar
  16. 16.
    Glick N (1978) Breaking records and breaking boards. Am Math Mon 85:2–26MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, ReadingMATHGoogle Scholar
  18. 18.
    Hall M, Christensen K, di Collabiano SA, Jensen HJ (2002) Time dependent extinction rate and species abundance in the Tangled Nature model of biological evolution. Phys Rev E 66:011904CrossRefGoogle Scholar
  19. 19.
    Hammann J, Bouchaud J-P, Dupuis V, Vincent E (2001) Separation of time and length scales in spin glasses: Temperature as a microscope. Phys Rev B 65:024439CrossRefGoogle Scholar
  20. 20.
    Hoffmann KH, Sibani P (1988) Diffusion in hierarchies. Phys Rev A 38:4261–4270MathSciNetCrossRefGoogle Scholar
  21. 21.
    Hérisson D, Ocio M (2002) Fluctuation‐dissipation ratio of a spin glass in the aging regime. Phys Rev Lett 88:257202Google Scholar
  22. 22.
    Jensen HJ (1998) Self‐Organized Complex Systems. Cambridge University Press, CambridgeMATHGoogle Scholar
  23. 23.
    Jonason K, Vincent E, Hammann J, Bouchaud JP, Nordblad P (1998) Memory and Chaos Effects in Spin Glasses. Phys Rev Lett 81:3243–3246CrossRefGoogle Scholar
  24. 24.
    Jönsson PE, Takayama H, Katori AH, Ito A (2005) Dynamical breakdown of the ising spin-glass order under a magnetic field. Phys Rev B 71:180412(R)Google Scholar
  25. 25.
    Katzgraber HG, Young AP (2005) Probing the Almeida‐Thouless line away from the mean-field model. Phys Rev B 72:184416CrossRefGoogle Scholar
  26. 26.
    Keller C, Kupfer H, Meier-Hirmer R, Wiech U, Selvamanickam V, Salama K (1990) Irreversible behaviour of oriented grained \( { yba2cu3ox } \). part 2: relaxation phenomena.Cryogenics 30:410–416CrossRefGoogle Scholar
  27. 27.
    Keller C, Kupfer H, Meier-Hirmer R, Wiech U, Selvamanickam V, Salama K (1990) Irreversible behaviour of oriented grained YBa2Cu3Ox. part 1: transport and shielding currents. Cryogenics 30:401–409CrossRefGoogle Scholar
  28. 28.
    Krug J (2007) Records in a changing world. cond-mat/0702136Google Scholar
  29. 29.
    Lundgren L, Nordblad P, Sandlund L (1986) Memory behaviour of the spin glass relaxation. Europhys Lett 1:529–534CrossRefGoogle Scholar
  30. 30.
    Mossa S, Ruocco G, Sciortino F, Tartaglia PP (2002) Quenches and crunches: does the system explore in ageing the same part of the configuration space explored in equilibrium? Phil Mag B 82:695–705Google Scholar
  31. 31.
    Nicodemi M, Jensen HJ (2001) Aging and memory phenomena in magnetic and transport properties of vortex matter: a brief review. J Phys A 34:8425MathSciNetMATHCrossRefGoogle Scholar
  32. 32.
    Oliveira LP, Jensen HJ, Nicodemi M, Sibani P (2005) Record dynamics and the observed temperature plateau in the magnetic creep rate of type ii superconductors. Phys Rev B 71:104526CrossRefGoogle Scholar
  33. 33.
    Parisi G (1979) Infinite number of order parameters for spin‐glasses. Phys Rev Lett 43:1754–1756CrossRefGoogle Scholar
  34. 34.
    Parisi G, Marinari E, Ruiz-Lorenzo JJ (1998) On the phase structure of the 3D Edwards-Anderson spin-glass. Phys Rev B 58:14852CrossRefGoogle Scholar
  35. 35.
    Redner S, Petersen MR (2007) Role of global warming on the statistics of record‐breaking temperatures. Phys Rev E 74:061114CrossRefGoogle Scholar
  36. 36.
    Rodriguez GF, Kenning GG, Orbach R (2003) Full Aging in Spin Glasses.Phys Rev Lett 91:037203CrossRefGoogle Scholar
  37. 37.
    Rudin W (1966) Real and complex analysis. McGraw Hill, New YorkMATHGoogle Scholar
  38. 38.
    Schön JC, Putz H, Jansen M (1996) Studying the energy hypersurface of continuous systems–the threshold algorithm. J Phys: Condens Matter 8:143–156Google Scholar
  39. 39.
    Sibani P (2006) Aging and intermittency in a p-spin model. Phys Rev E 74:031115CrossRefGoogle Scholar
  40. 40.
    Sibani P (2006) Mesoscopic fluctuations and intermittency in aging dynamics. Europhys Lett 73:69–75CrossRefGoogle Scholar
  41. 41.
    Sibani P, Andersen CM (2001) Aging and self‐organized criticality in driven dissipative systems. Phys Rev E 64:021103CrossRefGoogle Scholar
  42. 42.
    Sibani P, Brandt M, Alstrøm P (1998) Evolution and extinction dynamics in rugged fitness landscapes. Int J Modern Phys B 12:361–391Google Scholar
  43. 43.
    Sibani P, Dall J (2003) Log‐Poisson statistics and pure aging in glassy systems. Europhys Lett 64:8–14CrossRefGoogle Scholar
  44. 44.
    Sibani P, Jensen HJ (2005) Intermittency, aging and extremal fluctuations. Europhys Lett 69:563–569CrossRefGoogle Scholar
  45. 45.
    Sibani P, Littlewood PB (1993) Slow Dynamics from Noise Adaptation. Phys Rev Lett 71:1482–1485CrossRefGoogle Scholar
  46. 46.
    Sibani P, Pedersen A (1999) Evolution dynamics in terraced NK landscapes. Europhys Lett 48:346–352CrossRefGoogle Scholar
  47. 47.
    Sibani P, Rodriguez GF, Kenning GG (2006) Intermittent quakes and record dynamics in the thermoremanent magnetization of a spin-glass. Phys Rev B 74:224407CrossRefGoogle Scholar
  48. 48.
    Sibani P, Schmidt M, Alstrøm P (1995) Fitness optimization and decay of the extinction rate through biological evolution. Phys Rev Lett 75:2055–2058Google Scholar
  49. 49.
    Sibani P, Schriver P (1994) Phase‐structure and low‐temperature dynamics of short range Ising spin glasses. Phys Rev B 49:6667–6671CrossRefGoogle Scholar
  50. 50.
    Sibani P, Schön C, Salamon P, Andersson J-O (1993) Emergent hierarchical structures in complex system dynamics. Europhys Lett 22:479–485Google Scholar
  51. 51.
    Stillinger FH, Weber TA (1983) Dynamics of structural transitions in liquids. Phys Rev A 28:2408–2416CrossRefGoogle Scholar
  52. 52.
    Stillinger FH, Weber TA (1984) Packing Structures and Transitions in Liquids and Solids. Science 225:983–989CrossRefGoogle Scholar
  53. 53.
    Struik LCE (1978) Physical aging in amorphous polymers and other materials. Elsevier, New YorkGoogle Scholar
  54. 54.
    Swift MR, Bokil H, Travasso RDM, Bray AJ (2000) Glassy behavior in a ferromagnetic p-spin model. Phys Rev B 62:11494–11498CrossRefGoogle Scholar
  55. 55.
    Takayama H, Hukushima K (2002) Numerical Study on Aging Dynamics in 3D Ising Spin-Glass Model. III. Cumulative Memory and ‘Chaos’ Effects in the Temperature Shift Protocol. J Phys Soc JPN 71:3003–3010CrossRefGoogle Scholar
  56. 56.
    Tang C, Wiesenfeld K, Bak P, Coppersmith S, Littlewood P (1987) Phase Organization. Phys Rev Lett 58:1161–1164MathSciNetCrossRefGoogle Scholar
  57. 57.
    Van Kampen NG (1992) Stochastic Processes in Physics and Chemistry. North Holland, AmsterdamGoogle Scholar
  58. 58.
    Vincent E (1991) Slow dynamics in spin glasses and other complex systems. In: Ryan DH (ed) Recent progress in random magnets. McGill University, Montreal, pp 209–246Google Scholar
  59. 59.
    Vincent E, Hammann J, Ocio M, Bouchaud J-P, Cugliandolo LF (1996) Slow dynamics and aging in spin‐glasses. SPEC-SACLAY-96/048Google Scholar

Books and Reviews

  1. 60.
    Tinkham M (1998) Introduction to Superconductivity. Krieger, MelbourneGoogle Scholar
  2. 61.
    Drossel B (2001) Biological evolution and statistical physics. Adv Phys 50:209–295CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Paolo Sibani
    • 1
  • Henrik, Jeldtoft Jensen
    • 2
  1. 1.Institut for Fysik og KemiSDUOdenseDenmark
  2. 2.Department of MathematicsImperial College LondonLondonUK