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The Statistical Physics of Energy Landscapes: From Spin Glasses to Optimization

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Computational Statistical Physics
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Summary

The concept of energy ‘landscapes’ leads to a unified understanding of phenomena in a number of different complex physical systems. All these systems are characterized by an energy function which possesses many local minima separated by barriers as a function of the state variables. If depicted graphically, such an energy function looks very much like a mountainous landscape. Typical examples of such complex systems are spin glasses which show a wealth of interesting relaxation phenomena, but also a number of industrially important minimization problems, which have a mountainous cost function landscape. These problems are intimately related by the thermally activated relaxation dynamics on complex energy landscapes.

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References

  1. N.G. van Kampen: Stochastic Processes in Physics and Chemistry ( Elsevier, Amsterdam 1997 )

    Google Scholar 

  2. K. Binder, D.W. Heermann: Monte Carlo Simulation in Statistical Physics, Springer Series in Solid-State Sciences, Vol. 80 ( Springer, Berlin 1992 )

    Google Scholar 

  3. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller: J. Chem. Phys. 21, 1087 (1953)

    Article  ADS  Google Scholar 

  4. K.H. Fischer, J.A. Hertz: Spin Glasses ( Cambridge University Press, Cambridge 1991 )

    Book  Google Scholar 

  5. T. Klotz, S. Schubert, K.H. Hoffmann: J. Phys.: Condens. Matter 10, 6127 (1998)

    Article  ADS  Google Scholar 

  6. B. Andresen, K.H. Hoffmann, K. Mosegaard, J. Nulton, J.M. Pedersen, P. Sala-mon: J. Phys. France 49, 1485 (1988)

    Article  Google Scholar 

  7. H.A. Kramers: Physica (The Hague) 7, 284 (1940)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. K.H. Hoffmann, P. Sibani: Phys. Rev. A 38, 4261 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  9. K.H. Hoffmann, S. Grossmann, F. Wegner: Z. Phys. B 60, 401 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  10. P. Sibani: Phys. Rev. B 35, 8572 (1987)

    Article  ADS  Google Scholar 

  11. P. Sibani, K.H. Hoffmann: Europhys. Lett. 16, 423 (1991)

    Article  ADS  Google Scholar 

  12. C. Uhlig, K.H. Hoffmann, P. Sibani: Z. Phys. B 96, 409 (1995)

    Article  ADS  Google Scholar 

  13. L. Lundgren, P. Svedlindh, P. Nordblad, P. Beckman: Phys. Rev. Lett. 51, 911 (1983)

    Article  ADS  Google Scholar 

  14. M. Ocio, H. Bouchiat, P. Monod: J. Phys. Lett. France 46, 647 (1985)

    Google Scholar 

  15. P. Nordblad, P. Svedlindh, J. Ferre, M. Ayadi: J. Magn. Magn. Matter 59, 250 (1986)

    Article  ADS  Google Scholar 

  16. P. Svedlindh, P. Granberg, P. Nordblad, L. Lundgren, H.S. Chen: Phys. Rev. B 35, 268 (1987)

    Article  ADS  Google Scholar 

  17. N. Bontemps, R. Orbach: Phys. Rev. B 37, 4708 (1988)

    Article  ADS  Google Scholar 

  18. J. Hammann, M. Ocio, E. Vincent: `Attempt at a comprehensive description of the slow spin glass dynamics.’ In: Relaxation in Complex Systems and Related Topics ed. by I.A. Campbell, C. Giovanella (Plenum Press, New York 1990 ) pp. 11–21

    Google Scholar 

  19. C. Rossel, Y. Maeno, I. Morgenstern: Phys. Rev. Lett. 62, 681 (1989)

    Article  ADS  Google Scholar 

  20. K. Biljakovic, J.C. Lasjaunias, P. Monceau: Phys. Rev. Lett. 62, 1512 (1989)

    Article  ADS  Google Scholar 

  21. K.H. Hoffmann, T. Meintrup, C. Uhlig, P. Sibani: Europhys. Lett. 22, 565 (1993)

    Article  ADS  Google Scholar 

  22. P. Sibani, K.H. Hoffmann: Phys. Rev. Lett. 63, 2853 (1989)

    Article  ADS  Google Scholar 

  23. C. Schulze, K.H. Hoffmann, P. Sibani: Europhys. Lett. 15, 361 (1991)

    Article  ADS  Google Scholar 

  24. K.H. Hoffmann, S. Schubert, P. Sibani: Europhys. Lett. 38, 613 (1997)

    Article  ADS  Google Scholar 

  25. E. Vincent, J. Hammann, M. Ocio: `Slow dynamics in spin glasses and other complex systems.’ In: Saclay Internal Report SPEC/91–080, Centre d’études de Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France, October 1991; also in: Recent Progress in Random Magnets, ed. by D.H. Ryan ( World Scientific, Singapore 1992 )

    Google Scholar 

  26. E. Aarts, J. Korst: Simulated Annealing and Boltzmann Machines, Wiley Series in Discrete Mathematics and Optimization ( Wiley, New York 1989 )

    Google Scholar 

  27. P. Sibani, C. Schön, P. Salamon, J.-O. Andersson: Europhys. Lett. 22, 479 (1993)

    Article  ADS  Google Scholar 

  28. S. Kirkpatrick, C.D. Gelatt, M.P. Vecchi: Science 220 (4598), 671 (1983)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. V. Cerny: J. Optim. Theory Appl. 45, 41 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  30. R. Ettelaie, M.A. Moore: J. Phys. Lett. France 46, L893 (1983)

    Google Scholar 

  31. P. Slarry, G. Dreyfus: J. Phys. Lett. France 45, L39 (1983)

    Google Scholar 

  32. S.R. White: In Proceedings of the ICCD 1984 (IEEE 1984) p. 646

    Google Scholar 

  33. M.P. Vecchi, S. Kirkpatrick: In Proceedings of the IEEE Trans. Computer Aided Design CAD-2, IEEE Trans. CAD (IEEE 1983 ) p. 215

    Google Scholar 

  34. E. Bonomi, S.L. Lutton: SIAM Rev. 26, 551 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  35. R. Durbin, D. Willshaw: Nature 326, 689 (1987)

    Article  ADS  Google Scholar 

  36. P. Salamon, J.D. Nulton, J.R. Harland, J. Pedersen, G. Ruppeiner, L. Liao: Comp. Phys. Comm. 49, 423 (1988)

    Article  ADS  Google Scholar 

  37. S. Geman, D. Geman: IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI 6, 721 (1984)

    Article  MATH  Google Scholar 

  38. M.O. Jakobsen, K. Mosegaard, J.M. Pedersen: In Model Optimization in Exploration Geophysics 2, ed. by A. Vogel ( Friedrich Vieweg and Son, Braunschweig/Wiesbaden 1988 ) p. 361

    Google Scholar 

  39. K.H. Hoffmann, P. Sibani, J.M. Pedersen, P. Salamon: Appl. Math. Lett. 3, 53 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  40. K.H. Hoffmann, P. Salamon: J. Phys. A Math. Gen. 23, 3511 (1990)

    Article  ADS  MATH  Google Scholar 

  41. M. Christoph, K.H. Hoffmann: J. Phys. A Math. Gen. 26 (13), 3267 (1993)

    Article  ADS  Google Scholar 

  42. K. Ergenzinger, K.H. Hoffmann, P. Salamon: J. Appl. Phys. 77, 5501 (1995)

    Article  ADS  Google Scholar 

  43. G. Dueck, T. Scheuer: J. Comput. Phys. 90, 161 (1990)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. P. Moscato, J.F. Fontanari: Phys. Lett. A 146, 204 (1990)

    Article  ADS  Google Scholar 

  45. C. Tsallis: J. Stat. Phys. 52, 479 (1988)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  46. T.J.P. Penna: Phys. Rev. E 51, R1 (1995)

    Article  ADS  Google Scholar 

  47. C. Tsallis, D.A. Stariolo: Physica A 233, 395 (1996)

    Article  ADS  Google Scholar 

  48. A. Franz, K.H. Hoffmann: Threshold accepting as limit case for a modified Tsallis statistics. Submitted to Appl. Math. Lett. 2000

    Google Scholar 

  49. A. Franz, K.H. Hoffmann, P. Salamon: Phys. Rev. Lett. 86, 5219 (2001)

    Article  ADS  Google Scholar 

  50. K.H. Hoffmann, M. Christoph, M. Hanf: `Optimizing simulated annealing.’ In: Parallel Problem Solving from Nature, ed. by H.-P. Schwefel, R. Maenner ( Springer, Berlin 1991 )

    Google Scholar 

  51. I. Morgenstern, D. Würtz: Z. Phys. B 67, 397 (1987)

    Article  ADS  Google Scholar 

  52. S. Rees, R.C. Ball: J. Phys. A Math. Gen. 20, 1239 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  53. G. Ruppeiner, J.M. Pedersen, P. Salamon: J. Phys. I 1, 455 (1991)

    Google Scholar 

  54. R. Frost: Ebsa c library documentation, version 2.1 (San Diego Supercomputing Center 1994 )

    Google Scholar 

  55. K.H. Hoffmann, D. Würtz, C. de Groot, M. Hanf: `Concepts in optimizing simulated annealing schedules: an adaptive approach for parallel and vector machines.’ In: Parallel and Distributed Optimization, ed. by M. Grauer, D.B. Pressmar (1991) pp. 154–175

    Google Scholar 

  56. M. Grötschel: Preprint 38, Universität Augsburg, Augsburg (1984)

    Google Scholar 

  57. R. Tafelmayer, K.H. Hoffmann: Comp. Phys. Comm. 86, 81 (1995)

    Article  ADS  MATH  Google Scholar 

  58. P. Sibani, J.M. Pedersen, K.H. Hoffmann, P. Salamon: Phys. Rev. A 42, 7080 (1990)

    Article  ADS  Google Scholar 

Download references

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Hoffmann, K.H. (2002). The Statistical Physics of Energy Landscapes: From Spin Glasses to Optimization. In: Computational Statistical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04804-7_4

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  • DOI: https://doi.org/10.1007/978-3-662-04804-7_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07571-1

  • Online ISBN: 978-3-662-04804-7

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