  We consider the dynamics and thermodynamics of a pair of magnetic dipoles
interacting via their magnetic fields. We consider only the "spin" degrees of
freedom; the dipoles are fixed in space. With this restriction it is possible
to provide the general solution of the equations of motion in analytical form.
Thermodynamic quantities, such as the specific heat and the zero field
susceptibility are calculated by combining low temperature asymptotic series
and a complete high temperature expansion. The thermal expectation value of the
autocorrelation function is determined for the low temperature regime including
terms linear in $T$. Furthermore, we compare our analytical results with
numerical calculations based on Monte Carlo simulations.
