Abstract
This review covers several topics involving renormalization group ideas. The solution of the $s$-wave Kondo Hamiltonian, describing a single magnetic impurity in a nonmagnetic metal, is explained in detail. See Secs. VII-IX. "Block spin" methods, applied to the two dimensional Ising model, are explained in Sec. VI. The first three sections give a relatively short review of basic renormalization group ideas, mainly in the context of critical phenomena. The relationship of the modern renormalization group to the older problems of divergences in statistical mechanics and field theory and field theoretic renormalization is discussed in Sec. IV. In Sec. V the special case of "marginal variables" is discussed in detail, along with the relationship of the modern renormalization group to its original formulation by Gell-Mann and Low and others.
Keywords
PhysicsRenormalization groupRenormalizationDensity matrix renormalization groupIsing modelFunctional renormalization groupKondo effectHamiltonian (control theory)Critical phenomenaQuantum mechanicsTheoretical physicsMathematical physicsImpurityMathematics
Affiliated Institutions
Related Publications
Theory of dynamic critical phenomena
An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The co...
Density matrix formulation for quantum renormalization groups
A generalization of the numerical renormalization-group procedure used first by Wilson for the Kondo problem is presented. It is shown that this formulation is optimal in a cert...
Correlation Energy of a Free Electron Gas
The limits of validity of the correlation-energy calculations in the regions of high density, low density, and actual metallic electron densities are discussed. Simple physical ...
Critical behavior of the electrical resistivity in magnetic systems
The effect of critical fluctuations on the resistivity near magnetic and order-disorder phase transitions is discussed. It is shown that in all magnetic and electronic systems t...
Review of techniques in the large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>expansion for dilute magnetic alloys
Magnetic ions embedded in a nonmagnetic host exhibit a number of unusual low-temperature properties known collectively as the Kondo effect. Conventional small-parameter expansio...
Publication Info
- Year
- 1975
- Type
- article
- Volume
- 47
- Issue
- 4
- Pages
- 773-840
- Citations
- 4365
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
4365
OpenAlex
Cite This
Kenneth G. Wilson
(1975).
The renormalization group: Critical phenomena and the Kondo problem.
Reviews of Modern Physics
, 47
(4)
, 773-840.
https://doi.org/10.1103/revmodphys.47.773
Identifiers
- DOI
- 10.1103/revmodphys.47.773