Lattice with spins interacting with nearest neighbours to favour either alignment and anti-alignment, as a minimal model of a ferromagnet. It has many connections with other systems in Statistical physics, and Complex systems, due to the abstract nature of the model.

1D Ising model was solved by Ising and others.

A major breakthrough in statistical physics was the exact solution of the Ising model in two dimensions [107]. Onsager gave in 1944 a complete solution of the problem in zero external magnetic field.

But in three dimensions, Istrail has shown [108] that essentially all versions of the Ising model are computationally intractable across lattices and thus the 3D Ising model, in its full, is NP-complete.

For another model with many interesting connections, see Spin glass