Journal of Statistical Physics, Vol. 62, Nos. 3/4, 1991, p. 509-528.
The magnetic properties of the one-dimensional Hubbard model with a hardcore interaction on a ring (periodic boundary conditions) are investigated. At finite temperatures it is shown to behave up to exponentially small corrections as a pure paramagnet. An explicit expression for the ground-state degeneracies is derived. The eigenstates of this model are used to perform a perturbational treatment for large but finite interactions. In first order in U an effective Hamiltonian for the one-dimensional Hubbard model is derived, it is the Hamiltonian of the one-dimensional Heisenberg model with antiferromagnetic couplings between nearest neighbor spins. An asymptotic expansion for the ground-state energy is given. The results are valid for arbitrary densities of electrons.