The qubits represented by individual atomic ions are stored in stable internal energy levels, typically hyperfine spin states of the ground electronic confiduration. While these effective spins do not interact directly, they can be made to interact through the application of spin-dependent laser forces. For example, when a laser force pushes a single atomic ion up for one qubit state and down for the other qubit state, the ion now has a very strong electric dipole moment -- a single charge in two positions. This type of laser force is exactly that used for quantum logic gates in trapped ion quantum computing.
When such a spin-dependent laser force is simultaneously applied to a string of atomic ions, the interactions between this dipolar matter give rise to nontrivial phases of order and disorder in the system. Because the system is composed of a stationary crystal of atoms, we have the capability of measuring every possible spin-spin correlation to track the ground state, characterize various forms of entanglement, or measure dynamics of this coupled spin system. Moreover, the external control of the laser force allows for unpresidented control of form and range of the effective interaction between spins. In some cases the interaction is uniform across all ions, in others it falls of like a typical 1/r^3 dipolar decay, and we can also simulated almost anything in between.
There are a rich variety of spin Hamiltonians that can be simulated in the trapped ion system, from the general XYZ spin model, to nontrivial multidimensional Ising models. As the number of atomic ions is added to the crystal, we expect interesting phenomena to arise, such as ferromagnetism and anti-ferromagnetism over various ranges in the crystal, spin frustration, and "spin-liquid" behavior.
