Ising expansion for the Hubbard model

We develop series expansions for the ground state properties of the Hubbard model by introducing an Ising anisotropy into the Hamiltonian. For the two-dimensional square lattice half-filled Hubbard model, the ground state energy, local moment, sublattice magnetization, uniform magnetic susceptibility, and spin stiffness are calculated as a function of U/t, where U is the Coulomb constant and t is the hopping parameter. Magnetic susceptibility data indicate a crossover around U{}4 between spin density wave antiferromagnetism and Heisenberg antiferromagnetism. Comparisons with Monte Carlo simulations, random phase approximation result, and mean-field solutions are also made.