Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture
- 1 November 1971
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 4 (9), 3174-3183
- 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.Keywords
This publication has 11 references indexed in Scilit:
- Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical BehaviorPhysical Review B, 1971
- Renormalization Group and Strong InteractionsPhysical Review D, 1971
- Dynamic Scaling Theory for Anisotropic Magnetic Systems.Physical Review Letters, 1970
- Dynamic Scaling Theory for Anisotropic Magnetic SystemsPhysical Review Letters, 1970
- On the microscopic foundation of scaling lawsPhysics Letters A, 1969
- Scaling approach to anisotropic magnetic systems staticsThe European Physical Journal A, 1969
- High-Temperature Critical Indices for the Classical Anisotropic Heisenberg ModelPhysical Review B, 1968
- The theory of equilibrium critical phenomenaReports on Progress in Physics, 1967
- Static Phenomena Near Critical Points: Theory and ExperimentReviews of Modern Physics, 1967
- Quantum Electrodynamics at Small DistancesPhysical Review B, 1954