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 Mat. Sb. (N.S.), 1974, Volume 94(136), Number 1(5), Pages 16–48 (Mi msb3631)

Analyticity of the correlation functions for one-dimensional classical systems with power law decay of the potential

R. L. Dobrushin

Abstract: We consider the one-dimensional Gibbs states for one-dimensional lattice and continuous systems where the interaction potential decays according to a power law. It is shown that for such systems the specific free energy and the correlation functions depend analytically on the potential.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 23:1, 13–44

Bibliographic databases:

UDC: 519.272
MSC: Primary 82A25; Secondary 60G50, 60J25

Citation: R. L. Dobrushin, “Analyticity of the correlation functions for one-dimensional classical systems with power law decay of the potential”, Mat. Sb. (N.S.), 94(136):1(5) (1974), 16–48; Math. USSR-Sb., 23:1 (1974), 13–44

Citation in format AMSBIB
\Bibitem{Dob74} \by R.~L.~Dobrushin \paper Analyticity of the correlation functions for one-dimensional classical systems with power law decay of the potential \jour Mat. Sb. (N.S.) \yr 1974 \vol 94(136) \issue 1(5) \pages 16--48 \mathnet{http://mi.mathnet.ru/msb3631} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=416406} \zmath{https://zbmath.org/?q=an:0321.60086} \transl \jour Math. USSR-Sb. \yr 1974 \vol 23 \issue 1 \pages 13--44 \crossref{https://doi.org/10.1070/SM1974v023n01ABEH001712} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. A. Malyshev, “Cluster expansions in lattice models of statistical physics and the quantum theory of fields”, Russian Math. Surveys, 35:2 (1980), 1–62
2. H Spohn, J Phys A Math Gen, 19:4 (1986), 533
3. Herbert Spohn, “Effective mass of the polaron: A functional integral approach”, Annals of Physics, 175:2 (1987), 278
4. R. L. Dobrushin, M. R. Martirosyan, “Possibility of high-temperature phase transitions due to the many-particle nature of the potential”, Theoret. and Math. Phys., 75:2 (1988), 443–448
5. Volker Betz, Herbert Spohn, “A central limit theorem for Gibbs measures relative to Brownian motion”, Probab Theory Relat Fields, 131:3 (2005), 459
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