The Hubbard model, spin degeneracy and Ising spins

Abstract The Hubbard model is used as a starting point for a study of an electronic system with spin ½. Using a functional integral representation at half-filling it is demonstrated that the spin degeneracy is equivalent to dynamic Ising spins coupled to the fermions. A magnetic phase transition of the model is related to a transition of the Ising spins from a paramagnetic to an antiferromagnetic phase. A metal-insulator transition in the paramagnetic phase can be described within this approach by the Green's function of non-interacting fermions, coupled to Ising spins. This picture is compared with the earlier Ising spin representation of the Hubbard model by Hirsch and discussed in terms of a small hopping amplitude.