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Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture

Kenneth G. Wilson
Phys. Rev. B 4, 3174 – Published 1 November 1971
An article within the collection: Physical Review B 50th Anniversary Milestones
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Abstract

The Kadanoff theory of scaling near the critical point for an Ising ferromagnet is cast in differential form. The resulting differential equations are an example of the differential equations of the renormalization group. It is shown that the Widom-Kadanoff scaling laws arise naturally from these differential equations if the coefficients in the equations are analytic at the critical point. A generalization of the Kadanoff scaling picture involving an "irrelevant" variable is considered; in this case the scaling laws result from the renormalization-group equations only if the solution of the equations goes asymptotically to a fixed point.

  • Received 2 June 1971

DOI:https://doi.org/10.1103/PhysRevB.4.3174

©1971 American Physical Society

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This article appears in the following collection:

Physical Review B 50th Anniversary Milestones

These Milestone studies represent lasting contributions to physics by way of reporting significant discoveries, initiating new areas of research, or substantially enhancing the conceptual tools for making progress in the burgeoning field of condensed matter physics.

Authors & Affiliations

Kenneth G. Wilson

  • Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14850

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Vol. 4, Iss. 9 — 1 November 1971

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