  In this paper, we theoretically study the critical properties of the
classical spin-1 Ising model using two approaches: 1) the analytical
low-temperature series expansion and 2) the numerical Metropolis Monte Carlo
technique. Within this analysis, we discuss the critical behavior of one-, two-
and three-dimensional systems modeled by the first-neighbor spin-1 Ising model
for different types of exchange interactions. The comparison of the results
obtained according the Metropolis Monte Carlo simulations allows us to
highlight the limits of the widely used mean-field theory approach. We also
show, via a simple transformation, that for the special case where the bilinear
and bicubic terms are set equal to zero in the Hamiltonian the partition
function of the spin-1 Ising model can be reduced to that of the spin-1/2 Ising
model with temperature dependent external field and temperature independent
exchange interaction times an exponential factor depending on the other terms
of the Hamiltonian and confirm this result numerically by using the Metropolis
Monte Carlo simulation. Finally, we investigate the dependence of the critical
temperature on the strength of long-range interactions included in the Ising
Hamiltonian comparing it with that of the first-neighbor spin-1/2 Ising model.
