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 Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 4, Pages 619–639 (Mi tvp4317)

Gibbs state describing coexistence of phases for a three-dimensional Ising model

R. L. Dobrushin

Moscow

Abstract: We consider a three-dimensional Ising model with critical value of chemical potential and sufficiently small temperature. We prove the existence of an infinite set of different Gibbsian states in infinite volume. All these states are not translation invariant. Physically, they correspond to the situation where there are simultaneously two phases and their bound fluctuates near some plane. The states of such a type are impossible in the two-dimensional case.

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English version:
Theory of Probability and its Applications, 1973, 17:4, 582–600

Bibliographic databases:

Citation: R. L. Dobrushin, “Gibbs state describing coexistence of phases for a three-dimensional Ising model”, Teor. Veroyatnost. i Primenen., 17:4 (1972), 619–639; Theory Probab. Appl., 17:4 (1973), 582–600

Citation in format AMSBIB
\Bibitem{Dob72} \by R.~L.~Dobrushin \paper Gibbs state describing coexistence of phases for a three-dimensional Ising model \jour Teor. Veroyatnost. i Primenen. \yr 1972 \vol 17 \issue 4 \pages 619--639 \mathnet{http://mi.mathnet.ru/tvp4317} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=421546} \zmath{https://zbmath.org/?q=an:0275.60119} \transl \jour Theory Probab. Appl. \yr 1973 \vol 17 \issue 4 \pages 582--600 \crossref{https://doi.org/10.1137/1117073} 

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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. L. Kuz'min, “Small-parameter series for the surface tension in a lattice model”, Theoret. and Math. Phys., 76:3 (1988), 961–967
2. R. A. Minlos, “R. L. Dobrushin – one of the founders of modern mathematical physics”, Russian Math. Surveys, 52:2 (1997), 251–256
3. A. G. Basuev, “Ising model in half-space: A series of phase transitions in low magnetic fields”, Theoret. and Math. Phys., 153:2 (2007), 1539–1574
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