Multifractal phase transitions in the non-debye relaxation processes

Abstract

The multifractal measures of the relaxation-time distributions are analytically obtained for some typical non-Debye dielectric relaxation processes. The characteristics of the corresponding multifractal thermodynamics are discussed. It is shown that the probability of the relaxation times near the poles of their distribution function is fractal scaling. The corresponding Lipschitz-Hold singular exponent is, or can be, determined by the so-called shape parameters in the empirical dielectric relaxation formulas. The relationship to some analytical proofs of the empirical dielectric formulas based upon the fractal models is also analyzed. Some generalized multifractal phase transitions with interesting features are reported in this paper. The recent experiment results on the molten-crystal transition in organic glass systems are also discussed to support our conclusions.