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Renormalization theory and chaos exponents in random systems

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  • Ney-Nifle, M.
  • Hilhorst, H.J.

Abstract

In renormalization group theory, fixed points of random systems are characterized by fixed coupling constant distributions. We show that to each such distribution a chaos exponent, called generically ζ∗, may be assigned. Their eigenoperators (in a statistical sense) are random perturbations of the coupling constants at fixed thermodynamic parameters; we refer to these as disorder perturbations. The exponents ζ∗ may appear in physical quantities when variations of the thermodynamic parameters couple to disorder perturbations. These matters are discussed in the context of spin glasses, where the well-known zero-temperature chaos exponent ζ couples to temperature variations in the spin glass phase. We elucidate in detail the role, hitherto overlooked, of the critical chaos exponent ζc in the Ising spin glass.

Suggested Citation

  • Ney-Nifle, M. & Hilhorst, H.J., 1993. "Renormalization theory and chaos exponents in random systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 194(1), pages 462-470.
    • Handle: RePEc:eee:phsmap:v:194:y:1993:i:1:p:462-470
    DOI: 10.1016/0378-4371(93)90377-G
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    References listed on IDEAS

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    1. M. Husein Sawit, 1986. "Tingkat Upah Riil Buruh Tidak Terdidik Di Pedesaan Das Cimanuk: 1977 s/d 1983," Economics and Finance in Indonesia, Faculty of Economics and Business, University of Indonesia, vol. 34, pages 197-209.
    2. Brummelhuis, M.J.A.M. & Hilhorst, H.J., 1992. "How a random walk covers a finite lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 35-44.
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