Title: Hidden singularities in spontaneously polarized molecular solids

Authors: Andrew Cassidy, Frank P. Pijpers and David Field

Summary: Films of condensed dipolar molecules spontaneously polarise and harbour electric fields. The strength of the electric field generated depends on the growth temperature and this relationship is not always trivial. For some materials, the relationship between growth temperature and field strength passes through a minimum or maximum value, meaning that, count-intuitively, field strength can increase with deposition temperature.  In this article, we demonstrated that his phenomenon can be modelled by an equation which is continuous but which does not have a continuous differential. The singularity in the differential corresponds to the temperature at which the field strength passes through a maximum or minimum.

https://pubs.aip.org/aip/jcp/article/158/14/144501/2877894/Hidden-singularities-in-spontaneously-polarized