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TMF, 1975, Volume 25, Number 3, Pages 358–369 (Mi tmf4080)  

This article is cited in 25 scientific papers (total in 27 papers)

Phase diagrams of classical lattice systems

S. A. Pirogov, Ya. G. Sinai


Abstract: The method of constructing the phase diagrams for the large number of classical lattice systems is developed. For these systems we get the description of stable thermodynamical phases in terms of contour models. The general theory is applied to the investigation of the spontaneous symmetry breaking and to the construction of phase diagrams for some peculiar lattice models.

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English version:
Theoretical and Mathematical Physics, 1975, 25:3, 1185–1192

Bibliographic databases:

Received: 21.04.1975

Citation: S. A. Pirogov, Ya. G. Sinai, “Phase diagrams of classical lattice systems”, TMF, 25:3 (1975), 358–369; Theoret. and Math. Phys., 25:3 (1975), 1185–1192

Citation in format AMSBIB
\Bibitem{PirSin75}
\by S.~A.~Pirogov, Ya.~G.~Sinai
\paper Phase diagrams of classical lattice systems
\jour TMF
\yr 1975
\vol 25
\issue 3
\pages 358--369
\mathnet{http://mi.mathnet.ru/tmf4080}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=676316}
\transl
\jour Theoret. and Math. Phys.
\yr 1975
\vol 25
\issue 3
\pages 1185--1192
\crossref{https://doi.org/10.1007/BF01040127}


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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. D. G. Martirosyan, “The effective area of boundary conditions in the model of classical Ising ferromagnetism”, Russian Math. Surveys, 34:5 (1979), 239–240  mathnet  crossref  mathscinet
    5. 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
    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. 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
    8. 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
    9. 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
    10. 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
    11. 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
    12. 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
    13. 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
    14. 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
    15. 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
    16. 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
    17. 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
    18. 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
    19. 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
    20. 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
    21. 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
    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  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  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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