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

Abstract 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 > 0 . Numerical simulations of this model on a periodic space chain with 10 sites ( N =10) yield the energy spectra of the model at K J = 2 for D J = 1 and D J = 2 , thus helping us compare, for a broad range of temperature, how some (per site) thermodynamic functions with the same value of K J but distinct values of D J 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.