Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 006, 14 pages      hep-lat/0610043      http://dx.doi.org/10.3842/SIGMA.2007.006
Contribution to the Proceedings of the O'Raifeartaigh Symposium

Generalized Potts-Models and their Relevance for Gauge Theories

Andreas Wipf a, Thomas Heinzl b, Tobias Kaestner a and Christian Wozar a
a) Theoretisch-Physikalisches Institut, Friedrich-Schiller-University Jena, Germany
b) School of Mathematics and Statistics, University of Plymouth, United Kingdom

Received October 05, 2006, in final form December 12, 2006; Published online January 05, 2007

Abstract
We study the Polyakov loop dynamics originating from finite-temperature Yang-Mills theory. The effective actions contain center-symmetric terms involving powers of the Polyakov loop, each with its own coupling. For a subclass with two couplings we perform a detailed analysis of the statistical mechanics involved. To this end we employ a modified mean field approximation and Monte Carlo simulations based on a novel cluster algorithm. We find excellent agreement of both approaches. The phase diagram exhibits both first and second order transitions between symmetric, ferromagnetic and antiferromagnetic phases with phase boundaries merging at three tricritical points. The critical exponents ν and γ at the continuous transition between symmetric and antiferromagnetic phases are the same as for the 3-state spin Potts model.

Key words: gauge theories; Potts models; Polyakov loop dynamics; mean field approximation; Monte Carlo simulations.

pdf (1048 kb)   ps (1266 kb)   tex (1816 kb)

References

  1. Wozar C., Kaestner T., Wipf A., Heinzl T., Pozsgay B., Phase structure of Z3-Polyakov-loop models, Phys. Rev. D 74 (2006), 114501, 19 pages, hep-lat/0605012.
  2. Yaffe L.G., Svetitsky B., First order phase transition in the SU(3) gauge theory at finite temperature, Phys. Rev. D 26 (1982), 963-965.
  3. Bazavov A., Berg B.A., Velytsky A., Glauber dynamics of phase transitions: SU(3) lattice gauge theory, Phys. Rev. D 74 (2006), 014501, 12 pages, hep-lat/0605001.
  4. Ashkin J., Teller E., Statistics of two-dimensional lattices with four components, Phys. Rev. 64 (1942), 178-184.
  5. Potts R.B., Some generalized order-disorder transformations, Proc. Camb. Phil. Soc. 48 (1952), 106-109.
  6. Wu F.Y., The Potts model, Rev. Modern Phys. 54 (1982), 235-268.
  7. Yamaguchi C., Okabe Y., Three-dimensional antiferromagnetic q-state Potts models: application of the Wang-Landau algorithm, J. Phys. A: Math. Gen. 34 (2001), 8781-8794, cond-mat/0108540.
  8. Harris A.B., Mouritsen O.G., Berlinsky A.J., Pinwheel and herringbone structures of planar rotors with anisotropic interactions on a triangular lattice with vacancies, Can. J. Phys. 62 (1984), 915-934.
  9. Roepstorff G., Path integral approach to quantum physics, Springer, 1994.
  10. O'Raifeartaigh L., Wipf A., Yoneyama H., The constraint effective potential, Nuclear Phys. B 271 (1986), 653-680.
  11. Fujimoto Y., Yoneyama H., Wipf A., Symmetry restoration of scalar models at finite temperature, Phys. Rev. D 38 (1988), 2625-2634.
  12. Holland K., Wiese U.-J., The center symmetry and its spontaneous breakdown at high temperatures, in At the Frontier of Particle Physics - Handbook of QCD, Vol. 3, Editor M. Shifman, World Scientific, Singapore, 2001, 1909-1944, hep-ph/0011193.
  13. Buss G., Analytische Aspekte effektiver SU(N)-Gittereichtheorien, Diploma Thesis, Jena, 2004.
  14. Engels J., Mashkevich S., Scheideler T., Zinovjev G., Critical behaviour of SU(2) lattice gauge theory. A complete analysis with the c2-method, Phys. Rev. B 365 (1996), 219-224, hep-lat/9509091.
  15. Gliozzi F., Necco S., Critical exponents for higher-representation sources in 3d SU(3) gauge theory from CFT, hep-th/0605285.
  16. Heinzl T., Kaestner T., Wipf A., Effective actions for the SU(2) confinement-deconfinement phase transition, Phys. Rev. D 72 (2005), 065005, 14 pages, hep-lat/0502013.
  17. Polonyi J., Szlachanyi K., Phase transition from strong coupling expansion, Phys. Lett. B 110 (1982), 395-398.
  18. Carlsson J., McKellar B., SU(N) Glueball masses in 2+1 dimensions, Phys. Rev. D 68 (2003), 074502, 18 pages, hep-lat/0303016.
  19. Meinel R., Uhlmann S., Wipf A., Ward identities for invariant group integrals, hep-th/0611170.
  20. Wang J.S., Swendsen R.H., Kotecky R., Three-state antiferromagnetic Potts models: a Monte Carlo study, Phys. Rev. B 42 (1990), 2465-2474.
  21. Lawrie I., Sarbach S., Theorie of tricritical points, in Phase Transitions and Critical Phenomena, Vol. 9, Editors C. Domb and J. Lebowitz, Academic Press, 1984, 2-155.
  22. Landau D., Swendsen R., Monte Carlo renormalization-group study of tricritical behavior in two dimensions, Phys. Rev. B 33 (1986), 7700-7707.
  23. Dittmann L., Heinzl T., Wipf A., An effective lattice theory for Polyakov loops, JHEP 0406 (2004), 005, 27 pages, hep-lat/0306032.
  24. Heinzl T., Kaestner T., Wipf A., Wozar C., SU(3) effective Polyakov-loop dynamics, in preparation.
  25. Kim S., de Forcrand Ph., Kratochvila S., Takaishi T., The 3-state Potts model as a heavy quark finite density laboratory, PoSLAT2005, 2006, 166, 6 pages, hep-lat/0510069.

Previous article   Next article   Contents of Volume 3 (2007)