When do particle interactions lead to breakdown of the Thellier laws?

The Thellier-Thellier method requires the magnetic minerals in a rock to obey certain systematic laws called the Thellier laws. Louis Neel derived these laws for non-interacting single-domain particles in a weak field. If the field is strong or there is significant magnetostatic coupling between particles, the Thellier laws can break down. A homotopy method is used to calculate energy barriers of interacting, randomly oriented particles and the effect of interactions on blocking temperatures is calculated. The conditions for breakdown of the Thellier laws are determined.