Simulation of high-spin Heisenberg models in coupled cavities

We propose a scheme to realize the Heisenberg model of any spin in an arbitrary array of coupled cavities. Our scheme is based on a fixed number of atoms confined in each cavity and collectively applied constant laser fields, and is in a regime where both atomic and cavity excitations are suppressed. It is shown that as well as optically controlling the effective spin Hamiltonian, it is also possible to engineer the magnitude of the spin. Our scheme would open up a way to simulate otherwise intractable high-spin problems in many-body physics.