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Journal of Experimental and Theoretical Physics

, Volume 90, Issue 1, pp 144–152 | Cite as

Breakdown of renormalizability in the Kondo problem in the high-temperature expansion of the free energy

  • Yu. N. Ovchinnikov
  • A. M. Dyugaev
Solids

Abstract

It is shown that there are two energy scales in the Kondo problem: Tk and T0, one of which (Tk) is exponentially small in the coupling constant g. The second scale T0is proportional to the squared coupling constant. Perturbation theory is valid only in the region TT0. The point T0 is apparently the crossover from weak to strong coupling. The first indications of the breakdown of the hypothesis of only one energy scale in the Kondo problem appear in fourth order of perturbation theory.

Keywords

Spectroscopy Free Energy State Physics Field Theory Elementary Particle 
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.

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References

  1. 1.
    A. A. Abrikosov and A. A. Migdal, J. Low Temp. Phys. 3, 519 (1970).CrossRefGoogle Scholar
  2. 2.
    A. M. Tsvelick and P. B. Wigmann, Adv. Phys. 32, 453 (1983).CrossRefADSGoogle Scholar
  3. 3.
    N. Andrei and K. Furuya, Physics 55, 331 (1983).MathSciNetGoogle Scholar
  4. 4.
    Yu. N. Ovchinnikov and A. M. Dyugaev, Zh. Éksp. Teor. Fiz. 115, 1263 (1999) [JETP 88, 696 (1999)].Google Scholar
  5. 5.
    W. Felsch, Zeitschrift fur Physik B 29, 212 (1978).Google Scholar
  6. 6.
    Yu. N. Ovchinnikov, A. M. Dyugaev, P. Fulde, et al., Pis’ma Zh. Éksp. Teor. Fiz. 66, 184 (1997) [JETP Lett. 66, 195 (1997)].Google Scholar
  7. 7.
    A. A. Abrikosov, A. P. Gor’kov, and I. E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics (Fizmatgiz, Moscow, 1962; Prentice-Hall, Englewood Cliffs, NJ, 1963).Google Scholar
  8. 8.
    Yu. N. Ovchinnikov and A. M. Dyugaev, Pis’ma Zh. Éksp. Teor. Fiz. 70, 106 (1999) [JETP Lett. 70, 111 (1999)].Google Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2000

Authors and Affiliations

  • Yu. N. Ovchinnikov
    • 1
    • 2
  • A. M. Dyugaev
    • 1
    • 2
  1. 1.Max-Planck-Institutefor the Physics of Complex SystemsDresdenGermany
  2. 2.Landau Institute of Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow oblastRussia

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