New developments in the theory of the hopping conductivity of spatially random systems

At present the relevance of percolative transport to traditional glasses is being established. The electronic glasses represent (relatively) well defined systems in which the effects of e.g. 'interactions' and 'disorder' may be isolated, and for which the percolative aspects of transport are relatively well understood. Thus these systems (spatially random, SR, and variable-range hopping, VRH) can be useful as models for glassy conduction processes. However, some inconsistencies in the published theoretical descriptions of such systems exist, namely regarding the placement of the critical (scaling, or peak) frequency and the relationship of the frequency dependence of the AC conductivity to critical exponents from percolation theory. These questions are clarified here. Further conclusions about the nature of the scaling relationships between the AC and DC conductivities are drawn. The role of stochasticity, or randomness in the definition of the scaling frequency, is emphasized.