Abstract
In this lecture we introduce the concepts and tools of Statistical Mechanics using the Ising model of condensed matter physics, proposed about one century ago to explain magnetism, as a paradigm. The evocative power of this model brought the techniques of Statistical Mechanics to other fields, like brain models in Cognitive Science, Machine Learning Theory, and more recently to the analysis of models in Game Theory, Economy and Sociology.
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References
Balian R. From Microphysics to Macrophysics, Springer, 1992.
R. Baron et al., Chap. 16, this book.
Diu B., Guthmann C., Lederer D. and Roulet B. Eléments de physique statistique - Hermann, 1989.
S. Galam, Chap 25, this book.
J. A. Hertz, A. S. Krogh, and R. G. Palmer. Introduction to the Theory of Neural Computation, Santa Fe Books, 1991.
J. J. Hopfield. Neural networks and physical systems with emergent collective computational properties. Proc. Natl. Acad. Sci. USA 79 (1982) 2554–2588.
E. Ising, Beitrag zur Theorie des Ferromagnetismus, Zeitschrift für Physik 31 (1925) 253–258. (see the web site http://www.physik.tudresden.de/itp/members/kobe/isingconf.html for a biography and interesting informations)
E. T. Jaynes, Information Theory and Statistical Mechanics, Phys. Rev. 106 (1957) 620–630. (see web site http://bayes.wustl.edu/etj/etj.html for a biography and more informations)
E. T. Jaynes. Probability theory and maximum entropy. (on-line version at http://bayes.wustl.edu/)
S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi. Science 220 (1983) 671–680.
L. Landau and E. Lifchitz, Physique Statistique, Ed. MIR (1967).
S. K. Ma, Statistical Mechanics, World Scientific, 1985.
P. Peretto, An introduction to the modeling of neural networks, Cambridge University Press, Collection Alea Saclay, 1992.
D. Phan, M. B. Gordon and J. P. Nadal., Chap. 20, this book.
G. Toulouse. Theory of frustration effects in spin glasses: I. Communications on Physics 2 (1977) 115–119.
G. Weisbuch and D. Stauffer, Chap. 21, this book
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Gordon, M.B. (2004). An Introduction to Statistical Mechanics. In: Bourgine, P., Nadal, JP. (eds) Cognitive Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24708-1_8
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DOI: https://doi.org/10.1007/978-3-540-24708-1_8
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