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.
Preview
Unable to display preview. Download preview PDF.
References
S.F. Edwards and P.W. Anderson, J. Phys. F 5, 965 (1975)
D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975)
J.L. van Hemmen and R.G. Palmer, J. Phys. A 12, 563 (1979)
G. Györgyi and P. Ruján, J. Phys. C to appear
G. Parisi, Phys. Rev. Lett. 43, 1754 (1979). J. Phys. A 13, L115; 1101; 1887 (1980)
G. Toulouse, in Lecture Notes in Physics, Vol. 149 (Springer 1981)
R. Omari, J.J. Préjean and J. Souletie, J. Physique 44, 25 (1983)
G. Grinstein and D. Mukamel, Phys. Rev. B 27, 4503 (1983)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-13389-0_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13369-8
Online ISBN: 978-3-540-38925-5
eBook Packages: Springer Book Archive