Dynamics and thermodynamics of a pair of interacting magnetic dipoles

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 analytically or 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 and short times including terms linear in T. Furthermore, we have performed Monte Carlo simulations for the system under consideration and compared our analytical results with these.