Abstract
We solve the Glauber dynamics of the fully asymmetric SK-model and some of its extensions: Incorporation of random external fields and additional storage of a finite number of patterns. An analytical expression for theT=0 autocorrelation function of the equilibrium dynamics is derived and compared with the asymptotic exponential decay. The dynamical behaviour of the fully asymmetric SK-model is also investigated in a situation with nonequilibrium initial conditions. For weak correlations between the synaptic couplings a first order perturbation expansion is made yielding a finite relaxation time for the response function and a vanishing EA-order parameter if the asymmetry is high enough.
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References
Parisi, G.: J. Phys. A19, L675 (1986)
Ioffe, L.B., Feigelman, M.V.: JETP Lett.44, 189 (1986)
Hertz, J.A., Grinstein, G., Solla, S.A.: In: Neural networks for computing. Denker, J.S. (ed.): AIP Conf. Proc.151, 213 (1986)
Bausch, R., Janssen, H.K., Kree, R., Zippelius, A.: J. Phys. C19, L779 (1986)
Derrida, B., Gardner, E., Zippelius, A.: Europhys. Lett.4, 167 (1987);
Derrida, B., Nadal, J.P.: J. Stat. Phys.19, 993 (1987);
Derrida, B.: J. Phys. A20, L721 (1987)
Kree, R., Zippelius, A.: Phys. Rev. A36, 4421 (1987)
Crisanti, A., Sompolinsky, H.: Phys. Rev. A36, 4922 (1987)
Crisanti, A., Sompolinsky, H.: Phys. Rev. A37, 4865 (1988)
Gutfreund, H., Reger, J.D., Young, A.P.: J. Phys. A21, 2775 (1988)
Krauth, W., Nadal, J.P., Mézard, M.: J. Phys. A21, 2995 (1988)
Hopfield, J.J.: Proc. Natl. Acad. Sci. USA79, 2554 (1982)
Amit, D.J., Gutfreund, H., Sompolinsky, H.: Phys. Rev. A32, 1007 (1985);
Amit, D.J., Gutfreund, H., Sompolinsky, H.: Ann. Phys. (NY)173, 30 (1987)
Little, W.A.: Math. Biosci.19, 101 (1974)
McCulloch, W.A., Pitts, W.: Math. Biophys.5, 115 (1943)
Rieger, H., Schreckenberg, M., Zittartz, J.: J. Phys. A21, L263 (1988)
Sommers, H.J.: Phys. Rev. Lett.58, 1268 (1987)
Rieger, H., Schreckenberg, M., Zittartz, J.: Z. Phys. B—Condensed Matter72, 523 (1988)
Personnaz, L., Guyon, I., Dreyfus, G., Toulouse, G.: J. Stat. Phys.43, 411 (1986)
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Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln
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Rieger, H., Schreckenberg, M. & Zittartz, J. Glauber dynamics of the asymmetric SK-model. Z. Physik B - Condensed Matter 74, 527–538 (1989). https://doi.org/10.1007/BF01311399
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DOI: https://doi.org/10.1007/BF01311399