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Stability of critical behaviour, critical-exponent renormalization and first-order transitions

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  • Capel, H.W.
  • Den Ouden, L.W.J.
  • Perk, J.H.H.

Abstract

The critical behaviour of systems with short-range interactions in which the free energy has divergent second derivatives is shown to be unstable under small perturbations. The perturbations can arise from additional terms in the hamiltonian with a long-range nature, but also from hidden variables, subjected to constraints. In general there will be either critical-exponent renormalization or first-order transitions; in special cases one can also have more complicated multicritical behaviour. In the analysis use is made of Legendre transformations and homogeneity properties of the short-range system. The results are rather general and independent of specific properties of operators in the hamiltonian, or the nature and number of hidden variables.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:95:y:1979:i:3:p:371-416
    DOI: 10.1016/0378-4371(79)90024-4
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    References listed on IDEAS

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    4. Ghislain Deleplace, 1976. ""Production de marchandises par des marchandises." Une critique de l'économie politique ricardienne," Cahiers d'Économie Politique, Programme National Persée, vol. 3(1), pages 37-54.
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    6. 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.
    7. Klemm, A. & Zagrebnov, V.A., 1977. "A compressible Dicke model (exact solution)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 86(2), pages 400-416.
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    1. Perk, J.H.H. & Capel, H.W., 1980. "Time- and frequency-dependent correlation functions for the homogeneous and alternating-isotropic XY-models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 100(1), pages 1-23.

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