Communications in Mathematical Physics

, Volume 67, Issue 1, pp 17–42 | Cite as

Existence of long-range order in the Migdal recursion equations

  • P. M. Bleher
  • E. Žalys


A modification of XY — model is introduced for which Migdal recursion equation are exact. High- and low-temperature fixed points of these equations are investigated. As a result the existence of long-range order at low temperature and its absence at high temperature are proved rigorously for the model under consideration in the case when dimensiond>2.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Wilson, K.G., Kogut, I.: Phys. Rep.12C, 75–199 (1974)Google Scholar
  2. 2.
    Wilson, K.G.: Rev. Mod. Phys.47, 773 (1975)Google Scholar
  3. 3.
    Kadanoff, L.P.: Notes on Migdal's recursion formulas. Preprint, IBM Research Lab., Zürich, Switzerland (1976)Google Scholar
  4. 4.
    Patashinskij, A.Z., Pokrovskij, V.L.: Usp. Phys. Nauk.121, 55 (1977) (in Russian)Google Scholar
  5. 5.
    Migdal, A.A.: JETP69, 810 (1975) (in Russian)Google Scholar
  6. 6.
    Migdal, A.A.: JETP69, 1457 (1975) (in Russian)Google Scholar
  7. 7.
    Bleher, P.M., Sinai, Ja.G.: Commun. Math. Phys.33, 23–42 (1973)Google Scholar
  8. 8.
    Bleher, P.M., Sinai, Ja.G.: Commun. Math. Phys.45, 247 (1975)Google Scholar
  9. 9.
    Bleher, P.M.: Tr. Mosc. Math. Ob.33, 155 (1975) (in Russian)Google Scholar
  10. 10.
    Bleher, P.M.: Usp. Math. Nauk.32, 243 (1977) (in Russian)Google Scholar
  11. 11.
    Sinai, Ja.G.: Mathematical problems of the theory of phase transitions. Hungary (1979) (in press)Google Scholar
  12. 12.
    Watson, G.N.: A treatise on the theory of Bessel functions. New York: Repr. Cambridge Univ. Press; Macmillan 1945Google Scholar
  13. 13.
    Bateman, G., Erdelyi, A.: Higher trancendental functions, Vol. 2. New York, Toronto, London: McGraw-Hill 1955Google Scholar
  14. 14.
    Ginibre, J.: Commun. Math. Phys.16, 310 (1970)Google Scholar
  15. 15.
    Bleher, P.M.: The numerical solution of the approximate equations of Migdal's renormgroup. Preprint, Inst. Appl. Math., USSR Academy of Sciences, No. 48 (1976) (in Russian)Google Scholar
  16. 16.
    Asano, T.: Phys. Rev. Letters24, 1409 (1970)Google Scholar
  17. 17.
    Householder, A.S.: Principles of numerical analysis. New York, Toronto, London: McGraw-Hill 1953Google Scholar
  18. 18.
    Sarkar, S.: Phys. Rev. S16 (8), 2666 (1977)Google Scholar
  19. 19.
    Besov, O.V., Nikolskij, S.M., Iljin, V.P.: Integral representations of functions and imbedding theorems. Moscow: Nauka 1975 (in Russian)Google Scholar
  20. 20.
    Bleher, P.M., Žalys, E.: The investigation of low- and high-temperature fixed points in the Migdal's equations. Preprint, Inst. Appl. Math., USSR Academy of Sciences (1978) (in Russian)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • P. M. Bleher
    • 1
  • E. Žalys
    • 2
  1. 1.Institute of Applied MathematicsAcademy of SciencesMoscowUSSR
  2. 2.Institute of Mathematics and CyberneticsAcademy of Sciences of Lithuania SSRVilniusUSSR

Personalised recommendations