  In this article, the Curie-Weiss type behavior and the appearance of an
"interaction" or "ordering" temperature for a collection of magnetic
nanoparticles is explored theoretically. We show that some systems where an
interaction temperature is reported are too dilute for dipolar interactions to
play a role unless at least some of the particles are clumped together. We then
show using the most simple type of clumps (particle pairs) that positive and
negative interaction temperatures are possible due to dipolar interactions. The
clump orientation dramatically changes this result. Finally, we show that an
apparent interaction temperature can be measured in magnetic nanoparticle
systems that have no interactions between particles, due to some alignment of
anisotropy easy axes. These results show that nanoscale physical structures
affect the measured magnetic response of nanoparticles.
