  We study the ordering kinetics in $d=2$ ferromagnets which corresponds to
populated neuron activities with long-ranged interactions, $V(r)\sim r^{-n}$
associated with short-ranged interaction. We present the results from
comprehensive Monte Carlo (MC) simulations for the nonconserved Ising model
with $n\ge 2$. Our results of long-ranged neuron kinetics are consistent with
the same dynamical behavior of short-ranged case ($n > 4$). The calculated
characteristic length scale in long-ranged interaction is found to be $n$
dependent ($L(t)\sim t^{1/(n-2)}$), whereas short-ranged interaction follows
$L(t)\sim t^{1/2}$ law and approximately preserve universality in domain
kinetics. Further, we did the comparative study of phase ordering near the
critical temperature which follows different behaviours of domain ordering near
and far critical temperature but follows universal scaling law.
