RENORMALIZATION THEORY AND CHAOS EXPONENTS IN RANDOM-SYSTEMS

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 zeta*, 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 zeta* 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 zeta couples to temperature variations in the spin glass phase. We elucidate in detail the role, hitherto overlooked, of the critical chaos exponent zeta(c) in the Ising spin glass.