Stochastic matrix description of the glass transition

We present a model of the glass transition viewed as the agglomeration and growth of clusters forming a covalent network. The creation of new layers of atoms on the rims of the clusters is treated in a probabilistic way as a linear transformation (encoded in what is called a stochastic matrix) of a vector whose components represent the probability distribution of various sites found on the rim. The asymptotic limit of the statistics of sites in the network is given by the matrix eigenvector with eigenvalue equal to one. The model reproduces the modified Gibbs-DiMarzio equation with a system parameter that is comparable to the one observed experimentally for many chalcogenide glasses. Some other features of the glass transition process, like the form of the specific heat, are also obtained.