Ground State Metamorphosis for Yang-Mills Fields on a Finite Periodic Lattice

  • A. Gonzalez-Arroyo
  • J. Jurkiewicz
  • C. P. Korthals-Altes
Part of the NATO Advanced Study Institutes Series book series (volume 82)


We study the weak coupling behaviour of the partition function of non-abelian gauge fields on a finite lattice. Periodic boundary conditions are imposed. Two different power laws in the coupling β−1 arise for the partition function, when the dimension d of space time is larger or smaller than a critical dimension dc. For SU(2) dc = 4 and we find at this dimension power behaviour corrected by log β. The phenomenon is of practical importance in Monte Carlo simulations of the twisted action.


Partition Function Gauge Group Wilson Loop Free Boundary Condition Finite Lattice 
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.
    K.G. Wilson, Phys. Rev. D10, 2455 (1974).ADSGoogle Scholar
  2. 2.
    G.’t Hooft, Nucl. Phys. B153, 141 (1979).MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    J. Groeneveld, J. Jurkiewicz and C.P. Korthals Altes, Physica Scripta 23, 1022 (1981).MathSciNetADSMATHCrossRefGoogle Scholar
  4. G.’t Hooft, Comm. Math. Phys. 81, 267 (1981).MathSciNetADSMATHCrossRefGoogle Scholar
  5. 4.
    L.P. Kadanoff, Rev. Mod. Phys. 49, 267 (1977).MathSciNetADSCrossRefGoogle Scholar
  6. 5.
    G. Mack in “Recent developments in gauge theories”, G.’t Hooft et al. eds., Plenum Press, New York (1980).Google Scholar
  7. G. Munster, Nucl. Phys. B180 FS2, 23 (1981).ADSCrossRefGoogle Scholar
  8. 6.
    G.’t Hooft, Caltech Preprint 68/819 (1981).Google Scholar
  9. 7.
    J. Groeneveld et., Phys. Lett. 92B, 312 (1980).ADSGoogle Scholar
  10. G. Mack, E. Pietarinen, Phys. Lett. 94B, 397 (1980).ADSGoogle Scholar
  11. 8.
    B.E. Baaquie, Phys. Rev. Dl6, 2602 (1977).Google Scholar
  12. V.F. Müller, W. Rühl, Ann. of Phys. 133, 240 (1981).ADSCrossRefGoogle Scholar
  13. 9.
    A.M. Polyakov, JETP Lett. 20, 194 (1974).ADSGoogle Scholar
  14. G.’t Hooft, Nucl. Phys. B79, 276 (1974).MathSciNetCrossRefGoogle Scholar
  15. 10.
    A.M. Polyakov, Nucl. Phys. B120, 429 (1977).MathSciNetADSCrossRefGoogle Scholar
  16. G.’t Hooft, Phys. Rev. D14, 3432 (1976).ADSGoogle Scholar
  17. 11.
    M. Abramovitch, I.A. Steegun, Hand book of Mathematical Functions.Google Scholar
  18. 12.
    C.B. Lang, C. Rebbi, P. Salomonson, S. Skagerstam, CERN-TH 3021.Google Scholar
  19. E. Onofri, P. Menotti, CERN-TH 3026.Google Scholar
  20. A. Gonzalez-Arroyo, C.P. Korthals Altes, preprint Marseille CPT-81/P.1303, to be published in Nucl. Phys.Google Scholar
  21. 13.
    A. Gonzalez-Arroyo, J. Jurkiewicz, C.P. Korthals Altes, to be published.Google Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • A. Gonzalez-Arroyo
    • 1
    • 2
  • J. Jurkiewicz
    • 1
    • 3
  • C. P. Korthals-Altes
    • 1
    • 4
  1. 1.Centre de Physique Théorique, Section 2CNRSMarseilleFrance
  2. 2.Universidad Autonoma de MadridCanto Blanco, MadridSpain
  3. 3.Jagellonian UniversityCracowPoland
  4. 4.Centre de Physique de Theorique, Section 2CNRSFrance

Personalised recommendations