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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N.G. van Kampen: Stochastic Processes in Physics and Chemistry ( Elsevier, Amsterdam 1997 )
K. Binder, D.W. Heermann: Monte Carlo Simulation in Statistical Physics, Springer Series in Solid-State Sciences, Vol. 80 ( Springer, Berlin 1992 )
N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller: J. Chem. Phys. 21, 1087 (1953)
K.H. Fischer, J.A. Hertz: Spin Glasses ( Cambridge University Press, Cambridge 1991 )
T. Klotz, S. Schubert, K.H. Hoffmann: J. Phys.: Condens. Matter 10, 6127 (1998)
B. Andresen, K.H. Hoffmann, K. Mosegaard, J. Nulton, J.M. Pedersen, P. Sala-mon: J. Phys. France 49, 1485 (1988)
H.A. Kramers: Physica (The Hague) 7, 284 (1940)
K.H. Hoffmann, P. Sibani: Phys. Rev. A 38, 4261 (1988)
K.H. Hoffmann, S. Grossmann, F. Wegner: Z. Phys. B 60, 401 (1985)
P. Sibani: Phys. Rev. B 35, 8572 (1987)
P. Sibani, K.H. Hoffmann: Europhys. Lett. 16, 423 (1991)
C. Uhlig, K.H. Hoffmann, P. Sibani: Z. Phys. B 96, 409 (1995)
L. Lundgren, P. Svedlindh, P. Nordblad, P. Beckman: Phys. Rev. Lett. 51, 911 (1983)
M. Ocio, H. Bouchiat, P. Monod: J. Phys. Lett. France 46, 647 (1985)
P. Nordblad, P. Svedlindh, J. Ferre, M. Ayadi: J. Magn. Magn. Matter 59, 250 (1986)
P. Svedlindh, P. Granberg, P. Nordblad, L. Lundgren, H.S. Chen: Phys. Rev. B 35, 268 (1987)
N. Bontemps, R. Orbach: Phys. Rev. B 37, 4708 (1988)
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
C. Rossel, Y. Maeno, I. Morgenstern: Phys. Rev. Lett. 62, 681 (1989)
K. Biljakovic, J.C. Lasjaunias, P. Monceau: Phys. Rev. Lett. 62, 1512 (1989)
K.H. Hoffmann, T. Meintrup, C. Uhlig, P. Sibani: Europhys. Lett. 22, 565 (1993)
P. Sibani, K.H. Hoffmann: Phys. Rev. Lett. 63, 2853 (1989)
C. Schulze, K.H. Hoffmann, P. Sibani: Europhys. Lett. 15, 361 (1991)
K.H. Hoffmann, S. Schubert, P. Sibani: Europhys. Lett. 38, 613 (1997)
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 )
E. Aarts, J. Korst: Simulated Annealing and Boltzmann Machines, Wiley Series in Discrete Mathematics and Optimization ( Wiley, New York 1989 )
P. Sibani, C. Schön, P. Salamon, J.-O. Andersson: Europhys. Lett. 22, 479 (1993)
S. Kirkpatrick, C.D. Gelatt, M.P. Vecchi: Science 220 (4598), 671 (1983)
V. Cerny: J. Optim. Theory Appl. 45, 41 (1985)
R. Ettelaie, M.A. Moore: J. Phys. Lett. France 46, L893 (1983)
P. Slarry, G. Dreyfus: J. Phys. Lett. France 45, L39 (1983)
S.R. White: In Proceedings of the ICCD 1984 (IEEE 1984) p. 646
M.P. Vecchi, S. Kirkpatrick: In Proceedings of the IEEE Trans. Computer Aided Design CAD-2, IEEE Trans. CAD (IEEE 1983 ) p. 215
E. Bonomi, S.L. Lutton: SIAM Rev. 26, 551 (1984)
R. Durbin, D. Willshaw: Nature 326, 689 (1987)
P. Salamon, J.D. Nulton, J.R. Harland, J. Pedersen, G. Ruppeiner, L. Liao: Comp. Phys. Comm. 49, 423 (1988)
S. Geman, D. Geman: IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI 6, 721 (1984)
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
K.H. Hoffmann, P. Sibani, J.M. Pedersen, P. Salamon: Appl. Math. Lett. 3, 53 (1990)
K.H. Hoffmann, P. Salamon: J. Phys. A Math. Gen. 23, 3511 (1990)
M. Christoph, K.H. Hoffmann: J. Phys. A Math. Gen. 26 (13), 3267 (1993)
K. Ergenzinger, K.H. Hoffmann, P. Salamon: J. Appl. Phys. 77, 5501 (1995)
G. Dueck, T. Scheuer: J. Comput. Phys. 90, 161 (1990)
P. Moscato, J.F. Fontanari: Phys. Lett. A 146, 204 (1990)
C. Tsallis: J. Stat. Phys. 52, 479 (1988)
T.J.P. Penna: Phys. Rev. E 51, R1 (1995)
C. Tsallis, D.A. Stariolo: Physica A 233, 395 (1996)
A. Franz, K.H. Hoffmann: Threshold accepting as limit case for a modified Tsallis statistics. Submitted to Appl. Math. Lett. 2000
A. Franz, K.H. Hoffmann, P. Salamon: Phys. Rev. Lett. 86, 5219 (2001)
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 )
I. Morgenstern, D. Würtz: Z. Phys. B 67, 397 (1987)
S. Rees, R.C. Ball: J. Phys. A Math. Gen. 20, 1239 (1987)
G. Ruppeiner, J.M. Pedersen, P. Salamon: J. Phys. I 1, 455 (1991)
R. Frost: Ebsa c library documentation, version 2.1 (San Diego Supercomputing Center 1994 )
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
M. Grötschel: Preprint 38, Universität Augsburg, Augsburg (1984)
R. Tafelmayer, K.H. Hoffmann: Comp. Phys. Comm. 86, 81 (1995)
P. Sibani, J.M. Pedersen, K.H. Hoffmann, P. Salamon: Phys. Rev. A 42, 7080 (1990)
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive