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On the validity of the replica method and its application to Ising chain in random field

  • III. Random Systems
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Static Critical Phenomena in Inhomogeneous Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 206))

Abstract

Classical spin models in the presence of random interactions or external fields are considered. A general argument shows that the normal (non-Parisi-type) replica-trick is bound to yield the correct free energy provided that this latter is an analytic function of the strength ε of the random variables. As an illustration, the free energy of the one-dimensional Ising model in random external field is calculated up to sixth order in e by direct computation and also by the replica method, and the coincidence of the two results is demonstrated.

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A. Pękalski J. Sznajd

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© 1984 Springer-Verlag

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Sütõ, A., Zimányi, G.T. (1984). On the validity of the replica method and its application to Ising chain in random field. In: Pękalski, A., Sznajd, J. (eds) Static Critical Phenomena in Inhomogeneous Systems. Lecture Notes in Physics, vol 206. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13389-0_10

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  • DOI: https://doi.org/10.1007/3-540-13389-0_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13369-8

  • Online ISBN: 978-3-540-38925-5

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