  We study a spin-gas model, where N_S system qubits are interacting with N_B
bath qubits via many-body interactions. We consider multipartite Ising
interactions and show how the effect of decoherence depends on the specific
coupling between the system and its environment. For instance, we analyze the
influence of decohenerce induced by k-body interactions for different values of
k. Moreover, we study how the effect of decoherence depends on the correlation
between baths that are coupled to different individual system qubit and compare
Markovian with non-Markovian interactions. As examples we consider specific
quantum many-body states and investigate their evolution under several
different decoherence models. As a complementary investigation we study how the
coupling to the environment can be employed to generate a desired multipartite
state.
