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

We study the domain ordering kinetics in d = 2 ferromagnets which corresponds to populated neuron activities with both long-ranged interactions, V(r) ∼ r-n and short-ranged interactions. We present the results from comprehensive Monte Carlo (MC) simulations for the nonconserved Ising model with n ≥ 2, interaction range considering near and far neighbors. Our model results could represent the long-ranged neuron kinetics (n ≤ 4) in consistent with the same dynamical behaviour of short-ranged case (n ≥ 4) at far below and near criticality. We found that emergence of fast and slow kinetics of long and short ranged case could imitate the formation of connections among near and distant neurons. The calculated characteristic length scale in long-ranged interaction is found to be n independent (L(t) ∼ t1/(n-2)), whereas short-ranged interaction follows L(t) ∼ t1/2 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.