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On Kadanoff's approximate renormalization group transformation

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  • Knops, H.J.F.

Abstract

The fixed point structure resulting from the approximate renormalization group equations obtained by shifting bonds on the square Ising lattice is considered as a function of a free parameter h appearing in the definition of these equations. Next to the fixed point S considered by Kadanoff which is located in a symmetry plane two other “critical” fixed points A and B are found for h0.726. At the value h = 0.741, A crosses the fixed point S and vanishes together with the fixed point B at h = 0.726. Furthermore correction terms to the eigenvalues of the linearized renormalization group equations as obtained by Kadanoff are considered which arise if one chooses h to be optimal at all points of the coupling parameter space.

Suggested Citation

  • Knops, H.J.F., 1977. "On Kadanoff's approximate renormalization group transformation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 86(2), pages 448-456.
    • Handle: RePEc:eee:phsmap:v:86:y:1977:i:2:p:448-456
    DOI: 10.1016/0378-4371(77)90040-1
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    Cited by:

    1. De Alcantara Bonfim, O.F., 1985. "Mean field renormalization group analysis of the Blume-Capel model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 130(1), pages 367-373.
    2. Den Nijs, M.P.M., 1979. "The Kadanoff lowerbound renormalization transformation for the q-state Potts model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 95(3), pages 449-472.
    3. Micnas, Roman, 1979. "Application of the functional integral method to the classical and quantum spin models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(3), pages 403-441.
    4. den Nijs, M.P.M. & Knops, H.J.F., 1978. "Variational renormalization method and the Potts model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 93(3), pages 441-456.

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