Elastic properties of a network model of glasses

A standard model of glasses is shown to exhibit unexpected and remarkably simple elastic properties. For a sequence of networks of decreasing degree or coordination z, the number of zero-frequency vibrational modes (also called ``degrees of freedom'') increases as e^-z/ζ. A simple statistical model is given which illuminates this behavior. In addition, the elastic constant c₄₄ decreases as (z-z₀{)}^{{ν}}$; in certain cases other elastic constants also exhibit this behavior. These simple functional relationships appear to hold accurately for all z>${z}₀$, where ${z}₀$ is the critical average degree at which the elastic constants vanish.