Ordering Dynamics in Neuron Activity Pattern Model: An insight to Brain Functionality

Abstract: 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.