Spin lattice

A spin lattice assigns a classical or quantum spin degree of freedom to each site of a specified crystal lattice. The lattice specifies spatial organization, while the interaction graph specifies which spins couple. Nearest-neighbor models couple adjacent sites, but longer-range interactions are also possible.

For an Ising model, each site carries a two-valued spin variable. For a quantum Heisenberg model, spin operators have noncommuting components, and a typical interaction is $J{\sum }_{⟨ij⟩}{\mathbf{S}}_i\cdot {\mathbf{S}}_j$. The sign and geometry of the couplings determine whether neighboring preferences can be satisfied together or produce geometric frustration.