A method for distinguishing power-law and approximate power-law behavior in glassy relaxation: Ionic conducting glasses

Abstract

The question of whether an apparent power-law behavior in the ac conductivity of glasses is a real power-law, or is the product of a factor linear in the frequency and logarithmic corrections is important for the interpretation of the data. The former behavior is predicted by theories which invoke scaling relations a priori and attribute the frequency dependence to hierarchical scaling, multifractal scaling, or anomalous diffusion on fractal structures. The latter behavior is a natural result of a pair approximation. A simple procedure is suggested for the purpose of distinguishing the two possibilities. The procedure involves plots of the locus of ordered pairs of frequency and temperature for which the imaginary part of the dielectric constant is a constant.