The Hubbard solution to the Hubbard model showed a non-trivial metal-i
nsulator transition. The value of the one-particle density of states a
t the Fermi energy in that solution decreased continuously with increa
sing value of the Hubbard interaction and vanished at a critical value
of the interaction. Such a solution is derived from a planar model, a
s an approximation to the exact construction of the model's one-partic
le Green function.