Matrix models and parquet approximation


In this work we consider the comparison of planar and planar parquet approximations for zero-dimensional hermitian matrix models. We discuss how the parquet approach reproduces planar one for matrix model φ4, multi-trace model, two-matrix model and the Goldstone matrix model.

About the authors

Andrei O Shishanin

Peoples Friendship University of Russia

(к.ф.-м.н.), доцент, каф. экспериментальной физики; Российский университет дружбы народов; Peoples Friendship University of Russia


  1. Hooft G.'t. A planar diagram theory for strong interactions // Nucl. Phys. B., 1974. Vol. 72, no. 3. Pp. 461-473.
  2. Brézin E., Itzykson C., Parisi G., Zuber J. B. Planar diagrams // Commun. Math. Phys., 1978. Vol. 59, no. 1. Pp. 35-51.
  3. Aref'eva I. Ya., Zubarev A. P. Parquet approximation in large N matrix theories // Phys. Lett. B., 1996. Vol. 386, no. 1-4. Pp. 258-268, arXiv: hep-th/9605005.
  4. Das S. R., Dhar A., Sengupta A. M., Wadia S. R. New critical behavior in d = 0 large-N matrix models // Mod. Phys. Lett. A., 1990. Vol. 5, no. 13. Pp. 1041-1056.
  5. Шишанин А. О. Матричная многоследовая модель в паркетном приближении // Изв. вузов. Физика, 2005. № 12. С. 65-69
  6. Itzykson C., Zuber J. B. The planar approximation. II // J. Math. Phys., 1980. Vol. 21, no. 3. Pp. 411-421.
  7. Kazakov V. A. Ising model on a dynamical planar random lattice: exact solution // Phys. Lett. A., 1986. Vol. 119, no. 3. Pp. 140-144.
  8. Шишанин А. О. Решение паркетных уравнений для двуматричной модели // Изв. вузов. Физика, 2006. № 5. С. 92-95
  9. Shimamune Y. On the phase structure of large N matrix models and gauge models // Phys. Lett. B., 1982. Vol. 108, no. 6. Pp. 407-411.
  10. Cicuta G.M., Molinari L., Montaldi E. Large N phase transitions in low dimensions // Mod. Phys. Lett. A, 1986. Vol. 1, no. 2. Pp. 125-129.
  11. Shishanin A., Ziatdinov I. Parquet approximation for large-N matrix Higgs model // JHEP, 2003. Vol. 2003, no. 07, 032. 12 pp., arXiv: hep-th/0303169.



Abstract - 9

PDF (Russian) - 4



  • There are currently no refbacks.

Copyright (c) 2011 Samara State Technical University

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies