The geometrical nature of disorder and its elementary excitations

Abstract

We propose, on the basis of a geometrical analysis of frustating short-range order (in the line of references [2], and [3]), a model in which an amorphous body is made of two conjugated Frank networks, one of cylindrical domains, the other one of disclinations. A similar model could apply to the spin system of amorphous magnets, to the disordered blue phase of cholesterics and, in a dynamic version, to liquids. Consequences concerning the phonon elementary excitations are discussed, like the Bragg-like behaviour at k = π/ d, the rotons modes, and the low energy localized modes invoked in the heat capacity low temperature behaviour