Persisting correlations of a central spin coupled to large spin baths
  The decohering environment of a quantum bit is often described by the coupling to a large bath of spins. The quantum bit itself can be seen as a spin $S=1/2$ which is commonly called the central spin. The resulting central spin model describes an important mechanism of decoherence. We provide mathematically rigorous bounds for a persisting magnetization of the central spin in this model with and without magnetic field. In particular, we show that there is a well defined limit of infinite number of bath spins. Only if the fraction of very weakly coupled bath spins tends to 100\% does no magnetization persist. 
Urban Seifert, Philip Bleicker, Philipp Schering, Alexandre Faribault,   and G\"otz S. Uhrig
quant-ph