A model solid with a double-well potential at each site and intersite coupling J is considered, where J is sufficiently small that kT_C is much less than the depth kT₀ of the well. The effect of the local breaking of symmetry that occurs around T₀ is investigated for a single site. Anomalies are particularly noticeable in the oscillation frequencies, mean squared displacement and heat capacity. There are examples of materials and computer simulations that display such behaviour.