Advertisement

Infrared problems and phase transitions of continuous order in low-dimensional systems

  • J. Zittartz
I. One Dimensional Models
Part of the Lecture Notes in Physics book series (LNP, volume 65)

Abstract

The infrared problem is the strong response, in particular logarithmic divergencies in perturbation theoretical treatments, of a system to perturbations which couple to low-lying energy excitations. Because of connections between phase space and momentum dispersion such problems arise normally in 1 and 2 space dimensions. In a unified description we show the mathematical equivalence of infrared behaviour for the following model situations: 1) 1-d Fermi systems with general interactions, 2) 1-d Bose systems with “Sine-Gordon” interaction, 3) the 2-d magnetic (harmonic) rotator model, 4) the 2-d classical Coulomb plasma.

Infrared singular behaviour is characterized by power law singularities in thermodynamic quantities with singular (or critical) exponents which usually vary continuously with system parameters. Depending or. the physical interpretation of these parameters in the different situations, this implies: 1) and 2): singular ground-state properties, a special particle spectrum and instabilities for correlation functions; 3): the phase transition of continuous order for 2-d magnetic systems and other systems with continuous symmetry; 4) a smooth metal-insulator transition and special thermodynamic properties in the Coulomb plasma.

Keywords

Fermi System Rotator Model Infrared Behaviour Continuous Order Bose System 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1) E. Müller-Hartmann and J. Zittartz: Phys. Rev. Lett. 33, 893 (1974); Z. Physik B22, 59 (1975)Google Scholar
  2. (2) J. Zittartz: Z. Physik B23, 55, 63 (1976)Google Scholar
  3. (3) A. Luther and V. Emery: Phys. Rev. Lett. 33, 589 (1974)Google Scholar
  4. (4) S.T. Chui and P.A. Lee: Phys. Rev. Lett. 35, 315 (1975)Google Scholar
  5. (4a) H.U. Everts and H. Schulz: Z. Physik B22, 285 (1975)Google Scholar
  6. (5) J. Zittartz: Z. Physik B23, 277 (1976)Google Scholar
  7. (6) K.D. Schotte: Z. Physik 230, 99 (1970)Google Scholar
  8. (7) S. Coleman: Phys. Rev. D11, 2088 (1975)Google Scholar
  9. (8) J. Zittartz: to be publishedGoogle Scholar
  10. (9) P.W. Anderson and G. Yuval in: Magnetism Vol. V, ed. by H. Suhl, Academic Press N.Y., 1973Google Scholar
  11. (10) R. Baxter: Ann. Phys. (N.Y.) 70, 193 (1972)Google Scholar
  12. (11) J. Zittartz: to be publishedGoogle Scholar
  13. (12) J. Zittartz and B.A. Huberman: Solid State Comm. 18, 1373 (1976)Google Scholar
  14. (13) E.H.Hauge and P.C. Hemmer: Physica Norvegica 5, 209 (1971)Google Scholar
  15. (14) P.A. Lee: Phys. Rev. Lett. 34, 1247 (1975)Google Scholar
  16. (14a) H. Gutfreund and R.A. Klemm: Phys. Rev. B14, 1073 (1976)Google Scholar

Copyright information

© Akadémiai Kiadó 1977

Authors and Affiliations

  • J. Zittartz
    • 1
  1. 1.Institut für Theoretische PhysikUniversität KölnKölnGermany

Personalised recommendations