  A dynamic mean-field theory for spin ensembles (spinDMFT) at infinite
temperatures on arbitrary lattices is established. The approach is introduced
for an isotropic Heisenberg model with $S = \tfrac12$ and external field. For
large coordination numbers, it is shown that the effect of the environment of
each spin is captured by a classical time-dependent random mean-field which is
normally distributed. Expectation values are calculated by averaging over these
mean-fields, i.e., by a path integral over the normal distributions. A
self-consistency condition is derived by linking the moments defining the
normal distributions to spin autocorrelations. In this framework, we explicitly
show how the rotating wave approximation becomes a valid description for
increasing magnetic field. We also demonstrate that the approach can easily be
extended. Exemplarily, we employ it to reach a quantitative understanding of a
dense ensemble of spins with dipolar interaction which are distributed randomly
on a plane including static Gaussian noise as well.
