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Equilibrium equations for the class of continuous systems with positive-definite two-body interaction

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Literature Cited

  1. J. E. Mayer, J. Chem. Phys.,10, 629 (1942).

    Google Scholar 

  2. D. Ruelle, Statistical Mechanics, New York (1969).

  3. W. Klein, J. Math. Phys.,16, 1482 (1975).

    Google Scholar 

  4. L. A. Pastur, Teor. Mat. Fiz.,18, 233 (1974).

    Google Scholar 

  5. V. A. Zagrebnov and L. A. Pastur, Teor. Mat. Fiz.,36, 352 (1978).

    Google Scholar 

  6. V. A. Zagrebnov, J. Stat. Phys.,27(3), 577 (1982).

    Google Scholar 

  7. H. Morall, Physica (Utrecht) A,81, 469 (1975);87, 331 (1977).

    Google Scholar 

  8. H. O. Georgii, Canonical Gibbs Measures, Lecture Notes in Mathematics, Vol. 760, Springer (1979).

  9. J. Preston, Gibbs Fields, Lecture Notes in Mathematics, Vol. 53A, Springer (1976).

  10. Ya. G. Sinai, Theory of Phase Transitions. Rigorous Results [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  11. D. Ruelle, Ann. Phys. (N. Y.),25, 109 (1963).

    Google Scholar 

  12. D. Ruelle, Commun. Math. Phys.,68, 127 (1970).

    Google Scholar 

  13. R. L. Dobrushin, Funktsional. Analiz i Ego Prilozhen.,2, 44 (1968); Teor. Mat. Fiz.,4, 101 (1970).

    Google Scholar 

  14. R. L. Dobrushin and E. A. Pecherski, Lecture Notes in Mathematics, Vol. 1021, Springer, New York (1983), p. 97.

    Google Scholar 

  15. O. Klein, Commun. Math. Phys.,86, 227 (1982).

    Google Scholar 

  16. N. N. Bogolyubov and B. V. Khatset, Dokl. Akad. Nauk SSSR,66, 321 (1949); N. N. Bogolyubov, Selected Works in Three Volumes, Vol. 2 [in Russian], Naukova Dumka, Kiev (1970), pp. 494–498; N. N. Bogoyubov, D. Ya. Petrina, and B. V. Khatset, Teor. Mat. Fiz.,1, 251 (1969).

    Google Scholar 

  17. A. J. F. Siegert, Physica (Utrecht),26, 30 (1960).

    Google Scholar 

  18. J. Fröhlich, Commun. Math. Phys.,47, D33 (1976).

    Google Scholar 

  19. J. Fröhlich and Y. M. Park, Commun. Math. Phys.,57, 235 (1978).

    Google Scholar 

  20. D. Brydges, Commun. Math. Phys.,58, 313 (1978); D. Brydges and P. Federbush, Commun. Math. Phys.,73, 197 (1980); Commun. Math. Phys.,70, 161 (1979); J. Imbrie, Commun. Math. Phys.,87, 515 (1983).

    Google Scholar 

  21. J. Fröhlich and T. Spencer, J. Stat. Phys.,24, 527 (1981); Commun. Math. Phys.,81, 527 (1981).

    Google Scholar 

  22. J. R. Fontaine and Ph. A. Martin, J. Stat. Phys.,36, 163 (1984).

    Google Scholar 

  23. M. Aizenmann and Ph. A. Martin, Commun. Math. Phys.,78, 99 (1980); M. Aizenmann and J. Fröhlich, J. Stat. Phys.,36, 163 (1984).

    Google Scholar 

  24. S. Albeverio and R. Hoegh-Krohn, Commun. Math. Phys.,68, 95 (1979); R. Gielerak, J. Math. Phys. (in print).

    Google Scholar 

  25. R. Gielerak and B. Zegarlinski, Fortschr. Phys., 1 (1984).

  26. J. L. Lebowitz and A. Martin-Lof, Commun. Math. Phys.,25, 276 (1976); J. L. Lebowitz, Ruttgers University Preprint, Ruttgers (1975); J. Bricmont, J. R. Fontaine, and L. J. Landau, Commun. Math. Phys.,56, 281 (1977); A. Messager, S. Miracle, and Ch.-E. Pfister, Commun. Math. Phys.,58, 19 (1978).

    Google Scholar 

  27. Ch.-E. Pfister, Commun. Math. Phys.,86, 375 (1982); J. Fröhlich and Ch.-E. Pfister, Commun. Math. Phys.,89, 303 (1983).

    Google Scholar 

  28. X. X. Ngyen and H. Zessin, Math. Nachr.,88, 105 (1979).

    Google Scholar 

  29. J. Kerstan, K. Matthes, and J. Mecke, Infinitely Divisible Point Processes, Chichester (1978).

  30. R. Gielerak, Preprint R-17-85-770 [in Russian], JINR, Dubna (1985); Preprint R-17-85-771 [in Russian], JINR, Dubna (1985).

  31. R. Gielerak, Fortschr. Phys.,29(1), 19 (1981).

    Google Scholar 

  32. J. Ginibre, Commun. Math. Phys.,16, 310 (1970).

    Google Scholar 

  33. J. Fröhlich and Ch.-E. Pfister, Commun. Math. Phys.,81, 277 (1981); Ch. Gruber and P. A. Martin, Phys. Rev. Lett.,45, 853 (1980); Ann. Phys. (N.Y.),131, 56 (1981).

    Google Scholar 

  34. R. Gielerak, Fortschr. Phys., (in print).

  35. J. Dimock and J. Glimm, Adv. Math.,12, 58 (1974).

    Google Scholar 

  36. A. Lenard, J. Math. Phys.,4, 553 (1963);2, 682 (1961).

    Google Scholar 

  37. V. A. Zagrebnov, Teor. Mat. Fiz.,51, 389 (1982).

    Google Scholar 

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Joint Institute for Nuclear Research, Dubna. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 67, No. 2, pp. 289–303, May, 1986.

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Gielerak, R. Equilibrium equations for the class of continuous systems with positive-definite two-body interaction. Theor Math Phys 67, 507–517 (1986). https://doi.org/10.1007/BF01118157

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