Renormalization theory and chaos exponents in random systems

M. Ney-Nifle and H.J. Hilhorst

Physica A: Statistical Mechanics and its Applications, 1993, vol. 194, issue 1, 462-470

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.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:194:y:1993:i:1:p:462-470

DOI: 10.1016/0378-4371(93)90377-G

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