In this prototype theory of ferromagnetism—and of many other physical phenomena as well—a spin Si =±1 is assigned to each of N sites on a fixed lattice. The spins, which live on the vertices of the lattice, interact with one another by means of bonds (the links of the lattice). These have strengths Jij in energy units. In addition, the spins can interact with external fields Bi of arbitrary strengths. The total energy is then given by: $$H = - \sum {{J_{ij}}} {S_i}{S_j} - \sum {{B_i}} {S_i}$$ and can be directly evaluated in any of the 2N spin configurations. In the most familiar version of the Ising model, the interactions are limited to nearest-neighbors on the lattice and the magnetic field is homogeneous, Bi =constant.