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A common Ising version of the Edwards-Anderson model places Ising spins on a spin lattice with short-range, fixed random interactions $J_{ij}$. The displayed sum counts each interacting pair once; positive $J_{ij}$ favors equal spins, negative $J_{ij}$ favors opposite spins. Different samples retain different couplings. Quenched disorder describes this fixed-sample averaging.^[ref]

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.

A spin model assigns a discrete or continuous spin variable to each site of a spin lattice or vertex of a graph and gives interacting configurations a Boltzmann factor. Spin models describe collective order and phase transitions in magnetic and other many-body systems.