  In this study, critical behavior of low dimensional magnetic systems as
cyano-bridged Tb(III)-Cr(III) bimetallic assembly was investigated with the
mixed spin $3$- spin $3/2$ Ising model. The mixed spin Ising model is simulated
with Cellular Automaton cooling and heating algorithms on one-dimensional
lattices in periodic boundary conditions. The Ising model Hamiltonian includes
only antiferromagnetic nearest-neighbor interaction ($% J>0$). The mixed spin
system behaves like the isolated one-dimensional chain for zero magnetic field
($h=\frac{H}{J}=0$). In the presence of the magnetic field, the magnetization
is calculated using zero-field cooling ($ZFC$) and field cooling ($FC$)
processes. The one-dimensional Ising model results are compatible with the
cyano-bridged Tb(III)-Cr(III) bimetallic quasi-one dimensional assembly
[Tb(H_{2}O)_{2}(DMF)_{4}{ Cr(CN)_{6}}].H_{2}O(DMF=dimethylformamide) results.
