We show that in Frenkel (or anti-Frenkel) disordered AgCl, AgBr, AgI, PbF2 materials the anomalous conductivity increase prior to transition to the molten state (AgCl, AgBr) or to the superionic state (AgI, PbF2) can be quantitatively described by defect-defect interaction enthalpies following a cube root law. The correct continuous (PbF,) and, surprisingly, the first order phase transition temperatures (AgCl, AgBr; AgI) are also obtained in this way. Causes and consequences of the cube root law concerning (i) the melting behavior of ionic conductors, (ii) the influence of homogeneous doping on phase transition temperatures, (iii) the specific heat, (iv) the impact on interfacial effects, and (v) the kinetics of defect formation are briefly discussed.