  We study in detail the exact thermodynamics of the one-dimensional standard
and staggered spin-1 Ising models with a single-ion anisotropy term in the
presence of a longitudinal magnetic field at low temperatures. The results are
valid for the ferromagnetic and anti-ferromagnetic (AF) models and for positive
and negative values of the crystal field for $T>0$. Although the excited states
of the ferro and anti-ferro models are highly degenerate, we show that the
temperature required for reaching the first excited state in the classical
spin-1 ferro model gives a scale of temperature that permits fitting the
z-component of the magnetization only by the contribution of two ground states
of the model. This approximation is not true for the equivalent AF function due
to the fact that the AF model is gapless along the lines separating the phases
in its phase diagram at T=0. We relate the number of plateaus in the
magnetization of each model to their respective phase diagrams at T=0. The
specific heat per site of the AF model distinguishes, at low temperature, the
transitions $\mbox{A} \rightleftharpoons \mbox{E}$ and $\mbox{G}
\rightleftharpoons \mbox{E}$ as the external magnetic field is varied. The
exact Helmholtz free energy of the classical spin-1 model is mapped onto the
equivalent function of the ionic limit of the 1D extended Hubbard model by
proper transformations.

Statistical Mechanics