Abstract
When the neighbors of any ion in an insulator are displaced, they produce changes in the energy of the reference ion that are second order in the displacements. These energy changes correspond to indirect two- and three-body interactions among the reference ion and its neighbors. Ab initio and empirical estimates demonstrate that these indirect interactions have non-negligible effects on the lattice vibrations in insulators, allowing, for example, violation of the Cauchy relations in cubic crystals. Our results indicate a need to reexamine potential models in current use for insulators.
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