So far, we have assumed that the atoms do not interact with each other. Even though this is a reasonable assumption in the case of diamagnetic and paramagnetic substances, this assumption fails in the case of ferromagnetism, where the spins of the atom try to align with each other to the extent permitted by the thermal agitation. In this case, we have to consider the Hamiltonian of the ensemble of the atom. Such a Hamiltonian will contain all the terms described above for individual atoms and terms corresponding to the interaction among the pairs of the atom. Ising model is one of the simplest approximations of such pairwise interaction.
Here the two atoms of a pair are at . Their interaction  is determined by their distance vector . In order to simplify the calculation, it is often assumed that interaction happens between neighboring atoms only and  is a constant. The effect of such interaction is often approximated as a mean field and, in our case, the Weiss field.