Complex zeros of the partition function for two-dimensionalU(N) lattice gauge theories

  • K. S. Kölbig
  • W. Rühl


The complex zeros of the partition function for the two-dimensionalU(N) lattice gauge model in the variable β or ξ=N/β are calculated analytically for large β and numerically. The zeros formN trajectories which forN→∞ fill a domain of the ξ plane densely. This domain touches the real ξ axis at ξ=1 with a kink that causes the Gross-Witten phase transition.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K.G. Wilson: Phys. Rev. D10, 2445 (1974)Google Scholar
  2. 2.
    G. t'Hooft: Nucl. Phys. B72, 461 (1974)Google Scholar
  3. 3.
    D.J. Gross, E. Witten: Phys. Rev. D21, 446 (1980)Google Scholar
  4. 4.
    Y.Y. Goldschmidt: J. Math. Phys.21, 1842 (1980)Google Scholar
  5. 5.
    T.D. Lee, C.N. Yang: Phys. Rev.87, 404, 410 (1952)Google Scholar
  6. 6.
    G.N. Watson: A treatise on the theory of Bessel functions. Second edition, Chap. 7.23, Eq. (2) Cambridge: Cambridge University Press 1944Google Scholar
  7. 7.
    Ref. [6], Chap. 15.53Google Scholar
  8. 8.
    Numerical results for the zeros of ξ(β, 6) and ξ(β, 7) corresponding toN=12 andN=14 respectively, are contained in the preprint version of this article, CERN preprint TH 3125, (1981)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • K. S. Kölbig
    • 1
  • W. Rühl
    • 1
  1. 1.CERNGeneva 23Switzerland
  2. 2.Fachbereich Physik der Universität KaiserslauternKaiserslauternFederal Republic of Germany

Personalised recommendations