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.
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
\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://mathscinet.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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https://www.mathnet.ru/eng/tmf2976
https://www.mathnet.ru/eng/tmf/v12/i1/p115
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