Ising, Heisenberg and Hubbard models in relation to insulating and metallic ferro- and antiferro-magnets

The Ising model in low dimensions is used for ferromagnets to relate internal energy and entropy to the magnetization. While this is done throughout the ferromagnetic phase, the low temperature predictions are compared with microscopic elementary excitations theory for both insulating and metallic ferromagnets. The model predictions are oversimplified. The spin s = 1/2 Heisenberg model for an insulating antiferromagnet is then considered, starting from one dimension and building up a two-dimensional square lattice from lattice strips of variable width. Chemical approaches based an counting local spin-pairing patterns (or Kekule structures) are brought into contact with recent work on ladders, with both even and odd numbers of legs, in the context of high-T-c cuprates. Finally, the Hubbard model and the closely related t-J model are discussed. For the former, simple rules, again based on a chemical approach, are proposed for predicting the spin properties of the ground states and comparison is made with existing computer studies. The related t-J model is briefly considered in relation to carriers moving through antiferromagnetic assemblies as in the high-T-c materials.