The exact thermodynamics of the longitudinal S=1 Ising model with S_z ²  term

We calculate 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 for T>0. The results are valid for the ferromagnetic and anti-ferromagnetic models and for positive and negative values of the crystal field. We show the plateaus of the magnetization (staggered magnetization) for the standard (staggered) ferro and anti-ferromagnetic models at very low temperatures and the effect of increasing the temperature on such plateaus. The behaviour of the specific heat per site of these models is also presented in this region of temperature. We relate the number of plateaus in the magnetization of each model to their respective phase diagram at T=0.