Statistical mechanics of continuous random networks: A model glass transition

We present a statistical-mechanical theory of the formation of a macroscopic random network built from elementary units. These units represent atoms or small molecules that can form up to p permanent covalent bonds. As the number of formed bonds is increased, we observe a continuous phase transition from a fluid phase to a localised (i.e. glassy) phase that is marked by the emergence of random static fluctuations in the atomic position and bond orientation densities. By using a variational ansatz we calculate the thermal (i.e. mainly entropic) fluctuations of the positions and bond orientations within the glassy phase.