Communications in Mathematical Physics

, Volume 32, Issue 4, pp 269–289

Analyticity of correlation functions in one-dimensional classical systems with slowly decreasing potentials

  • R. L. Dobrushin
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dobrushin, R. L.: Description of a random field by means of conditional probabilities and regularity conditions. Probability theory and applications (in Russian)13 (2) 201–222 (1968).Google Scholar
  2. 2.
    Dobrushin, R. L.: Problem of uniqueness of a Gibbs random field and phase transitions. Functional Analysis and applications (in Russian)2 (4) 44–57 (1968).Google Scholar
  3. 3.
    Dobrushin, R. L.: Gibbs field: the general case. Functional analysis and applications (in Russian)3 (1) 27–35 (1969).Google Scholar
  4. 4.
    Ruelle, D.: Statistical mechanics of one-dimensional lattice gas, Commun. math. Phys.,9, (4) 267–278 (1968).Google Scholar
  5. 5.
    Ibragimov, I. A., Linnik, J. V.: Independent and stationnary dependent variables (In Russian) Science edit. 1965.Google Scholar
  6. 6.
    Dyson, F. J.: Existence of a phase transitions in one-dimensional Ising Ferromagnet,Commun. math. Phys.,12, (1) 91–107 (1969).Google Scholar
  7. 7.
    Fisher, M. E., Felderhof, B. U.: Phase transition in one-dimensional cluster-interaction fluids, IA, IB, II, III, Ann. Phys.,58, (1) 176–300 (1970).Google Scholar
  8. 8.
    Gallavotti, G., Miracle-Sole, S., Ruelle, D.: Absence of phase transition in one-dimensional systems with hard core, Phys. Lett.,A26, (8) 350–351 (1970).Google Scholar
  9. 9.
    Gallavotti, G., Miracle-Sole, S.: Absence of phase transitions in hard-core one-dimensional systems with long-range interactions, Journ. of Math. Phys.,11, (1) 147–154 (1969).Google Scholar
  10. 10.
    Ruelle, D.: Statistical mechanics-rigorous results, N.Y.-Amsterdam: W. A. Benjamin Inc., 1969.Google Scholar
  11. 11.
    Van Hove, L.: Sur l'intégrale de configuration pour les systèmes de particules à une dimension, Physica,16, 137–143 (1950).Google Scholar
  12. 12.
    Araki, H.: Gibbs states of one dimensional quantum lattice, Commun. math. Phys.,14, (2) 120–157, 1969.Google Scholar
  13. 13.
    Statuliavičus, V. A.: On limit theorems for stochastic functions I. Lithuanian Mathematical Collection (in Russian)10, (3) 583–592 (1970).Google Scholar
  14. 14.
    Žurbenko, I. G.: On the determination of mixed semi-invariants for some classes of random processes (in Russian) Theor. Prob. Appl.15 (3), 541–544 (1970).Google Scholar
  15. 15.
    Gallavotti, G.: Lin, T. F.: One dimensional lattice gases with rapidly decreasing interaction, Archive for Ration. Mech. and Analys.,37, (3) 181–191 (1970).Google Scholar
  16. 16.
    Feller, W.: An introduction to Probability Theory and its applications, vol. 1, New York: Wiley & Sons Inc., 1950.Google Scholar
  17. 17.
    Dobrushin, R. L.: Gibbs random fields for lattice systems with pair interactions. Functional analysis and applications (in Russian)2 (4) 31–43 (1968).Google Scholar
  18. 18.
    Lanford, O. E., Ruelle, D.: Observables at infinity and states with short-range correlations in statistical mechanics, Commun. math. Phys.,13, (3) 194–215 (1968).Google Scholar
  19. 19.
    Dunford, N., Schwartz, T.: Linear operators, Part 1, General Theory, New York-London: Interscience Publishers, 1958.Google Scholar
  20. 20.
    Gunning, R. G., Rossi, H.: Analytic functions of several complex variables, New York: Prentice Hall, 1965.Google Scholar
  21. 21.
    Shabat, B. V.: Introduction to complex analysis (in Russian) Science edit. 1669.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • R. L. Dobrushin
    • 1
    • 2
  1. 1.Institute for Problems of Information-TransmissionMoskvaUSSR
  2. 2.Mathematics Department Chair of Probability TheoryMoscow State UniversityMoscowUSSR

Personalised recommendations