Comparison of the exact thermodynamics of the AF Blume–Emery–Grifiths and of the spin-1 ferromagnetic Ising models

We study in detail the thermodynamics of the anti-ferromagnetic Blume–Emery–Griffiths (AF BEG) model in the presence of a longitudinal magnetic field. Its thermodynamics is derived from the exact Helmholtz free energy (HFE) of the model, valid for T>0T>0. Numerical simulations of this model on a periodic space chain with 10 sites (N  =10) yield the energy spectra of the model at KJ=2 for DJ=1 and DJ=2, thus helping us compare, for a broad range of temperature, how some (per site) thermodynamic functions with the same value of KJ but distinct values of DJ behave, namely: the z  -component of the magnetization, the specific heat and the entropy. These thermodynamic functions of the AF BEG model at K|J|=2 are compared to those of the spin-1 ferromagnetic Ising model with D|J|>1.5, for which the T=0 phase diagrams of both models are identical. This comparison is done in a large interval of temperature.