Abstract
We continue the analysis of hierarchical interfaces in random media started in earlier work. We show that from the estimates on the renormalized random variables established in that work, it follows that these models possess unique Gibbs states describing mostly flat interfaces in dimensionD > 3, if the disorder is weak and the temperature low enough. In the course of the proof we also present very explicit formulas for expectations of local observables.
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References
A. Bovier and C. Külske, Stability of hierarchical interfaces in a random field model,J. Stat. Phys. 69:79 (1992).
A. Bovier and P. Picco, Stability of interfaces in random environments: A renormalization group analysis of a hierarchical model,J. Stat. Phys. 62:177 (1991).
H. O. Georgii, Gibbs measures and phase transitions, inStudies in Mathematics, Vol. 9 (de Gruyter, Berlin, 1988).
Ch. Külske, Ph.D. Thesis, Ruhr-Universität Bochum, (1993).
Ya. G. Sinai,Theory of Phase Transitions: Rigorous Results (Pergamon Press, Oxford, 1982).
W. Stout,Almost Sure Convergence (Academic Press, New York, 1974).
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Bovier, A., Külske, C. Hierarchical interfaces in random media II: The Gibbs measures. J Stat Phys 73, 253–266 (1993). https://doi.org/10.1007/BF01052760
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DOI: https://doi.org/10.1007/BF01052760