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Variational principles in renormalization theory

Author

Listed:
  • Van Saarloos, W.
  • Van Leeuwen, J.M.J.
  • Pruisken, A.M.M.

Abstract

The variational principles introduced by Kadanoff et al. in the renormalization theory are analyzed. It is shown that the values for the specific heat critical exponent α which can be found by a variational method are restricted to α < 0 or α = 1 (first order transition). The reason is the confluence of the singularities in the free energy and in the variational parameters. A full implementation of the variational principle changes for the square Ising lattice the earlier obtained α = 0.001756 to α = −0.123413.

Suggested Citation

  • Van Saarloos, W. & Van Leeuwen, J.M.J. & Pruisken, A.M.M., 1978. "Variational principles in renormalization theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 92(3), pages 323-342.
    • Handle: RePEc:eee:phsmap:v:92:y:1978:i:3:p:323-342
    DOI: 10.1016/0378-4371(78)90135-8
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    Cited by:

    1. Capel, H.W. & Den Ouden, L.W.J. & Perk, J.H.H., 1979. "Stability of critical behaviour, critical-exponent renormalization and first-order transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 95(3), pages 371-416.
    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. Igloi, F. & Vanderzande, C., 1986. "Renormalisation group study of the (2+1) dimensional Potts model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 135(2), pages 347-358.

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