  Central spin models describe several types of solid state nanostructures
which are presently considered as possible building blocks of future quantum
information processing hardware. From a theoretical point of view, a key issue
remains the treatment of the flip-flop terms in the Hamiltonian in the presence
of a magnetic field. We systematically study the influence of these terms, both
as a function of the field strength and the size of the spin baths. We find
crucial differences between initial states with central spin configurations of
high and such of low polarizations. This has strong implications with respect
to the influence of a magnetic field on the flip-flop terms in central spin
models of a single and more than one central spin. Furthermore, the
dependencies on bath size and field differ from those anticipated so far. Our
results might open the route for the systematic search for more efficient
perturbative treatments of central spin problems.
