Scenario for the Vogel-Fulcher "law"

A scenario is presented to explain the Vogel-Fulcher "law" which describes the slowing down of relaxation processes associated with many glasses: ${\tau }^{-1\mathrm{}}=\tau _0^{}{}_{}{}^{-1\mathrm{}}\exp \left[\frac{-E}{(T-T_0)}\right]$. It assumes that relaxation processes are local and satisfy an Arhennius law whose activation energy $E_a$ is determined by the energy needed to jump out of a local potential well. This latter is determined by employing a local Landau expansion of the free energy in powers of the order parameter, where it is assumed that frustration and quenched-in randomness lead to local order which is incompatible with global order. In the free energy, the randomness is considered to provide a linear coupling which drives the quadratic term, with the quartic term preventing the divergence at $T_0$ from actually occurring.