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TMF, 1976, Volume 26, Number 1, Pages 61–76 (Mi tmf3169)  

This article is cited in 26 scientific papers (total in 28 papers)

Phase diagrams of classical lattice systems continuation

S. A. Pirogov, Ya. G. Sinai

Abstract: III. Contour Models
In this section we introduce contour models and study some of their properties. In $Sec$. V we shall show that every pure thermodynamic phase which we construct can be described by means of a suitably chosen contour model. In the language of contour models one can clearly elucidate what is meant by the expression “typical configurations of every phase are small perturbations of a corresponding ground state”.

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English version:
Theoretical and Mathematical Physics, 1976, 26:1, 39–49

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Received: 21.04.1975

Citation: S. A. Pirogov, Ya. G. Sinai, “Phase diagrams of classical lattice systems continuation”, TMF, 26:1 (1976), 61–76; Theoret. and Math. Phys., 26:1 (1976), 39–49

Citation in format AMSBIB
\by S.~A.~Pirogov, Ya.~G.~Sinai
\paper Phase diagrams of classical lattice systems continuation
\jour TMF
\yr 1976
\vol 26
\issue 1
\pages 61--76
\jour Theoret. and Math. Phys.
\yr 1976
\vol 26
\issue 1
\pages 39--49

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    This publication is cited in the following articles:
    1. D. G. Martirosyan, “K voprosu ob otsenke sverkhu chisla periodicheskikh gibbsovskikh sostoyanii dlya modeli reshetchatogo gaza”, UMN, 30:6(186) (1975), 181–182  mathnet  mathscinet
    2. D. Ruelle, “On manifolds of phase coexistence”, Theoret. and Math. Phys., 30:1 (1977), 24–29  mathnet  crossref  mathscinet
    3. I. A. Kashapov, “Structure of ground states in three-dimensional using model with three-step interaction”, Theoret. and Math. Phys., 33:1 (1977), 912–918  mathnet  crossref  mathscinet
    4. A. G. Basuev, “Gas of “connected configurations” and allowance for the “hard-core” potential of contours in the Mayer expansion of a gas of lattice-model contours”, Theoret. and Math. Phys., 57:3 (1983), 1178–1189  mathnet  crossref  mathscinet  isi
    5. A. G. Basuev, “Mayer expansions for gas of contours at low temperatures and in arbitrary external fields for the multicomponent ising model”, Theoret. and Math. Phys., 58:1 (1984), 80–91  mathnet  crossref  mathscinet  isi
    6. A. G. Basuev, “Complete phase diagrams with respect to external fields at low temperatures for models with nearest-neighbor interaction in the case of a finite or countable number of ground states”, Theoret. and Math. Phys., 58:2 (1984), 171–182  mathnet  crossref  mathscinet  isi
    7. D. G. Martirosyan, “Uniqueness of Gibbs states in lattice models with one ground state”, Theoret. and Math. Phys., 63:2 (1985), 511–518  mathnet  crossref  mathscinet  isi
    8. A. G. Basuev, “Hamiltonian of the phase separation border and phase transitions of the first kind. I”, Theoret. and Math. Phys., 64:1 (1985), 716–734  mathnet  crossref  mathscinet  isi
    9. S. A. Pirogov, “Coexistence of phases in a multicomponent lattice liquid with complex thermodynamic parameters”, Theoret. and Math. Phys., 66:2 (1986), 218–221  mathnet  crossref  mathscinet  isi
    10. S. N. Isakov, “Phase diagrams and singularity at the point of a phase transition of the first kind in lattice gas models”, Theoret. and Math. Phys., 71:3 (1987), 638–648  mathnet  crossref  mathscinet  isi
    11. A. G. Basuev, “Hamiltonian of the phase separation border and phase transitions of the first kind. II. The simplest disordered phases”, Theoret. and Math. Phys., 72:2 (1987), 861–871  mathnet  crossref  mathscinet  isi
    12. S. P. Novikov, L. A. Bunimovich, A. M. Vershik, B. M. Gurevich, E. I. Dinaburg, G. A. Margulis, V. I. Oseledets, S. A. Pirogov, K. M. Khanin, N. N. Chentsova, “Yakov Grigor'evich Sinai (on his sixtieth birthday)”, Russian Math. Surveys, 51:4 (1996), 765–778  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    13. N. N. Ganikhodzhaev, U. A. Rozikov, “Discription of periodic extreme Gibbs measures of some lattice models on the Cayley tree”, Theoret. and Math. Phys., 111:1 (1997), 480–486  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. N. N. Ganikhodzhaev, U. A. Rozikov, “Group representation of the Cayley forest and some of its applications”, Izv. Math., 67:1 (2003), 17–27  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. N. N. Ganikhodzhaev, C. H. Pah, “Phase diagrams of multicomponent lattice models”, Theoret. and Math. Phys., 149:2 (2006), 1512–1518  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    16. Rozikov, UA, “A constructive description of ground states and Gibbs measures for Ising model with two-step interactions on Cayley tree”, Journal of Statistical Physics, 122:2 (2006), 217  crossref  isi
    17. G. I. Botirov, U. A. Rozikov, “Potts model with competing interactions on the Cayley tree: The contour method”, Theoret. and Math. Phys., 153:1 (2007), 1423–1433  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. A. G. Basuev, “Interphase Hamiltonian and first-order phase transitions: A generalization of the Lee–Yang theorem”, Theoret. and Math. Phys., 153:1 (2007), 1434–1457  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    19. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    20. Mukhamedov, F, “On contour arguments for the three state Potts model with competing interactions on a semi-infinite Cayley tree”, Journal of Mathematical Physics, 48:1 (2007), 013301  crossref  isi
    21. Ganikhodjaev, NN, “PIROGOV-SINAI THEORY WITH NEW CONTOURS FOR SYMMETRIC MODELS”, International Journal of Geometric Methods in Modern Physics, 5:4 (2008), 537  crossref  mathscinet  zmath  isi
    22. Rozikov, UA, “A contour method on Cayley trees”, Journal of Statistical Physics, 130:4 (2008), 801  crossref  mathscinet  zmath  adsnasa  isi
    23. Eugene Pechersky, Elena Petrova, Sergey Pirogov, “Phase transitions of laminated models at any temperature”, Mosc. Math. J., 10:4 (2010), 789–806  mathnet  crossref  mathscinet
    24. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001  crossref  isi
    25. A. I. Bufetov, B. M. Gurevich, K. M. Khanin, F. Cellarosi, “The Abel Prize award to Ya. G. Sinai”, Russian Math. Surveys, 69:5 (2014), 931–956  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    26. Lebowitz J.L. Bonolis L., “A life in statistical mechanics”, Eur. Phys. J. H, 42:1 (2017), 1–21  crossref  isi  scopus
    27. U. A. Rozikov, F. Kh. Khaidarov, “Four competing interactions for models with an uncountable set of spin values on a Cayley tree”, Theoret. and Math. Phys., 191:3 (2017), 910–923  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    28. Yu. Kh. Eshkabilov, G. I. Botirov, F. H. Haydarov, “Phase transitions for models with a continuum set of spin values on a Bethe lattice”, Theoret. and Math. Phys., 205:1 (2020), 1372–1380  mathnet  crossref  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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