Evolution of covalent networks under cooling: contrasting the rigidity window and jamming scenarios

We study the evolution of structural disorder under cooling in supercooled liquids, focusing on covalent networks. We introduce a model for the energy of networks that incorporates weak non-covalent interactions. We show that at low-temperature, these interactions considerably affect the network topology near the rigidity transition that occurs as the coordination increases. As a result, this transition becomes mean-field and does not present a line of critical points previously argued for, the "rigidity window". Vibrational modes are then not fractons, but instead are similar to the anomalous modes observed in packings of particles near jamming. These results suggest an alternative interpretation for the intermediate phase observed in chalcogenides.