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Variational renormalization method and the Potts model

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  • den Nijs, M.P.M.
  • Knops, H.J.F.

Abstract

The variational principle is presented for a continuous renormalization transformation. It is shown that a strict application of the variational method leads to a singularity in the variational parameter which is related to that in the free energy. The equations governing the behaviour of the variational parameter can, in the continuous formulation (for a single coupling parameter), be cast in a differential form from which it can be seen that the method will predict either a very weak singularity (α < 0) or a first order transition. A numerical study of the q-state Potts model is presented which shows that as q increases to 4 the model just fails to exhibit the expected first-order transition.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:93:y:1978:i:3:p:441-456
    DOI: 10.1016/0378-4371(78)90165-6
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    References listed on IDEAS

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    1. Den Nijs, M.P.M. & Pruisken, A.M.M. & Van Leeuwen, J.M.J., 1976. "Critical phenomena for a triangular spin lattice I," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(3), pages 539-556.
    2. 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.
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