
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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Theoretical and Mathematical Physics, 1972, 12:1, 699–711
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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 115134
\mathnet{http://mi.mathnet.ru/tmf2976}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=479233}
\transl
\jour Theoret. and Math. Phys.
\yr 1972
\vol 12
\issue 1
\pages 699711
\crossref{https://doi.org/10.1007/BF01030046}
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This publication is cited in the following articles:

R. L. Dobrushin, “Conditions for the absence of phase transitions in onedimensional classical systems”, Math. USSRSb., 22:1 (1974), 28–48

S. A. Pirogov, Ya. G. Sinai, “Phase diagrams of classical lattice systems”, Theoret. and Math. Phys., 25:3 (1975), 1185–1192

S. A. Pirogov, “The existence of lattice models with several types of pariticles”, Math. USSRIzv., 9:6 (1975), 1333–1357

S. A. Pirogov, Ya. G. Sinai, “Phase diagrams of classical lattice systems continuation”, Theoret. and Math. Phys., 26:1 (1976), 39–49

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

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