  The Blume-Emery-Griffiths model with the dipol-quadrupol interaction (\ell)
has been simulated using a cellular automaton algorithm improved from the
Creutz cellular automaton (CCA) on the face centered cubic (fcc) lattice. The
finite-size scaling relations and the power laws of the order parameter (M) and
the susceptibility (\chi) are proposed for the dipol-quadrupol interaction
(\ell). The dipol-quadrupol critical exponent \delta_{\ell} has been estimated
from the data of the order parameter (M) and the susceptibility (\chi). The
simulations have been done in the interval 0\leq \ell =L/J\leq 0.01 for
d=D/J=0, k=K/J=0 and h=H/J=0 parameter values on a face centered cubic (fcc)
lattice with periodic boundary conditions. The results indicates that the
effect of the \ell parameter is similar to the external magnetic field (h). The
critical exponent \delta_{\ell}$ are in good agreement with the universal value
(\delta_{h}=5) of the external magnetic field.
