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TMF, 1972, Volume 12, Number 1, Pages 115–134 (Mi tmf2976)  

This article is cited in 5 scientific papers (total in 5 papers)

Asymptotic behavior of Gibbsian distributions for lattice systems and its dependence on the form of the volume

R. L. Dobrushin


Abstract: A study is made of the cases for which the existence of Gibbsian states in an infinite lattice was proved in earlier papers. It is proved that Gibbstan states exist in an infinite region, which may be part of the complete lattice, and an investigation is made of the dependence of the correlation functions on the form of the region. The second term in the asymptotic behavior of the free energy, which depends on the form of the region, is found. Finally, some properties of correlation weakening for such Gibbsian states are investigated.

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English version:
Theoretical and Mathematical Physics, 1972, 12:1, 699–711

Bibliographic databases:

Received: 22.07.1971

Citation: R. L. Dobrushin, “Asymptotic behavior of Gibbsian distributions for lattice systems and its dependence on the form of the volume”, TMF, 12:1 (1972), 115–134; Theoret. and Math. Phys., 12:1 (1972), 699–711

Citation in format AMSBIB
\Bibitem{Dob72}
\by R.~L.~Dobrushin
\paper Asymptotic behavior of Gibbsian distributions for lattice systems and its dependence on the form of the volume
\jour TMF
\yr 1972
\vol 12
\issue 1
\pages 115--134
\mathnet{http://mi.mathnet.ru/tmf2976}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=479233}
\transl
\jour Theoret. and Math. Phys.
\yr 1972
\vol 12
\issue 1
\pages 699--711
\crossref{https://doi.org/10.1007/BF01030046}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. L. Dobrushin, “Conditions for the absence of phase transitions in one-dimensional classical systems”, Math. USSR-Sb., 22:1 (1974), 28–48  mathnet  crossref  mathscinet  zmath
    2. S. A. Pirogov, Ya. G. Sinai, “Phase diagrams of classical lattice systems”, Theoret. and Math. Phys., 25:3 (1975), 1185–1192  mathnet  crossref  mathscinet
    3. S. A. Pirogov, “The existence of lattice models with several types of pariticles”, Math. USSR-Izv., 9:6 (1975), 1333–1357  mathnet  crossref  mathscinet
    4. S. A. Pirogov, Ya. G. Sinai, “Phase diagrams of classical lattice systems continuation”, Theoret. and Math. Phys., 26:1 (1976), 39–49  mathnet  crossref  mathscinet
    5. V. A. Arzumanian, B. S. Nakhapetian, S. K. Pogosyan, “Asymptotic expansion of the logarithm of the partition function in spin lattice systems that possess a vacuum”, Theoret. and Math. Phys., 81:1 (1989), 1134–1141  mathnet  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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