The classical limit ofn-vector spin models
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Abstract
It is proved that the free energy of a system ofn-dimensional spins with Kac type potential is equal, in the infinite range zero strength limit, to the free energy of the corresponding Curie-Weiss system in which every spin interacts equally with every other spin.
Keywords
Neural Network Free Energy Statistical Physic Complex System Nonlinear Dynamics
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References
- 1.Lebowitz, J. L., Penrose, O.: J. Math. Phys.7, 98 (1966)Google Scholar
- 2.Thompson, C. J.: Mathematical statistical mechanics, Appendix C. Macmillan N.Y. 1972.Google Scholar
- 3.Stanley, H. E.: Phys. Rev. Lett.20, 589 (1968)Google Scholar
- 4.Stanley, H. E.: Phys. Rev.176, 718 (1968)Google Scholar
- 5.Kac, M., Thompson, C. J.: Physica Norvegica5, 163 (1971)Google Scholar
- 6.Silver, H., Frankel, N. E., Ninham, B. W.: J. Math. Phys.13, 468 (1972)Google Scholar
- 7.Cramer, H.: Mathematical methods in statistics, p. 118. Princeton University Press 1951.Google Scholar
- 8.Grenander, U., Szegö, G.: Toeplitz forms and their applications. Berkeley, California: University of California Press 1958.Google Scholar
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