Magnetic susceptibility and low-temperature specific-heat of integrable 1-D Hubbard model under open-boundary conditions

The magnetic susceptibility and the low-temperature specific heat of the 1-dimensional Hubbard model under the integrable open-boundary conditions are discussed through the Bethe ansatz with the string hypothesis. The contributions of the boundary fields to both the susceptibility and the specific heat are obtained, and their exact expressions are analytically derived.