BULK AND SURFACE FLOPPY MODES

In this paper most of the ideas that have been put forward over the past ten years on constraint counting and the resultant floppy modes in random networks are collected together. It is shown how model systems can help us understand the phenomena via rigidity percolation. These ideas have been tested experimentally in bulk glasses where the most illuminating experiments involve low frequency phonons as seen by inelastic neutron scattering in chalcogenide glasses. Other experiments, such as measurements of the elastic moduli, have been disappointing in that the effects are not resolved. Marginal cases where the instability is caused by the surface, leading to the number of floppy modes scaling with the surface area, are also examined. These effects may be important in porous silica, zeolites and possibly biological systems.