  We study the decoherence of a central spin 1/2 induced by a spin bath with
intrabath interactions. Since we are interested in the cumulative effect of
interaction and disorder, we study baths comprising Ising spins with random
ferro- and antiferromagnetic interactions between the spins. Using the
resolvent operator method which goes beyond the standard Born-Markov master
equation approach, we show that, in the weak coupling regime, the decoherence
of the central spin at all times is entirely determined by the local-field
distribution or equivalently, the dynamical structure factor of the Ising bath.
We present analytic results for the Ising spin chain bath at arbitrary
temperature for different distributions of the intrabath interaction strengths.
We find clear evidence of non-Markovian behavior in the low temperature regime.
We also consider baths described by Ising models on higher-dimensional
lattices. We find that interactions lead to a significant reduction of the
decoherence. An important feature of interacting spinbaths is the saturation of
the asymptotic Markovian decay rate at high temperatures, as opposed to the
conventional Ohmic boson bath.
