Thermodynamic scaling theory for impurities in metals

Phys. Rev. B 30, 2806 – Published 1 September 1984
H. R. Krishna-Murthy and C. Jayaprakash


A perturbative scaling theory for calculating static thermodynamic properties of arbitrary local impurity degrees of freedom interacting with the conduction electrons of a metal is presented. The basic features are developments of the ideas of Anderson and Wilson, but the precise formulation is new and is capable of taking into account band-edge effects which cannot be neglected in certain problems. Recursion relations are derived for arbitrary interaction Hamiltonians up to third order in perturbation theory. A generalized impurity Hamiltonian is defined and its scaling equations are derived up to third order. The strategy of using such perturbative scaling equations is delineated and the renormalization-group aspects are discussed. The method is illustrated by applying it to the single-impurity Kondo problem whose static properties are well understood.


  • Received 15 December 1981
  • Published in the issue dated 1 September 1984

© 1984 The American Physical Society

Authors & Affiliations

H. R. Krishna-Murthy

  • Department of Physics, Indian Institute of Science, Bangalore 560012, India

C. Jayaprakash*

  • IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598

  • *Present address: Department of Physics, Ohio State University, Columbus, Ohio 43210.

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