  We show that atoms trapped in micro-cavities that interact via exchange of
virtual photons can model an anisotropic Heisenberg spin-1/2 chain in an
external magnetic field. All parameters of the effective Hamiltonian can
individually be tuned via external lasers. Since the occupation of excited
atomic levels and photonic states are strongly suppressed, the effective model
is robust against decoherence mechanisms, has a long lifetime and its
implementation is feasible with current experimental technology. The model
provides a feasible way to create cluster states in these devices.
