Edwards-Anderson model ($H_J(s)=-{\sum }_{\{i,j\}}{J}_{ij}{s}_i{s}_j$)

A common Ising version of the Edwards-Anderson model places Ising spins on a 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]