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Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture
Phys. Rev. B 4, 3174 – Published 1 November, 1971
DOI: https://doi.org/10.1103/PhysRevB.4.3174
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.
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Comments & Replies
Renormalization-Group Verification of Crossover with Respect to the Lattice Anisotropy Parameter
See Also
Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior
Addendum to "Renormalization-group verification of crossover with respect to the lattice anisotropy parameter": Systems with first- and second-neighbor interactions
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- L. P. Kadanoff (private communication)
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