Abstract
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) ∼ t 1/(n−2)), whereas short-ranged interaction follows L(t) ∼ 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.
Highlights
Brain is a complex system that works through an interplay of neurons
We address two important questions in this context via kinetic Monte Carlo (MC) simulations: (a) What is the growth law for ordering phases of neurons? Is the growth law independent of the range of interaction? (b) What is the morphology for ordering phases of neurons, as measured by the correlation function and structure factor? Is it comparable for all interaction range? We will be providing the answers to the above questions from our extensive MC simulations
We study the effect of interaction range on the morphology of neuron activity pattern
Summary
Brain is a complex system that works through an interplay of neurons. The spiking activity in complex neuron network in brain is dynamic (far from equilibrium) [1]. Spontaneous and simultaneous connections among near and distant neurons is an inherent property underlying brain functionality, as the domain formed by longrange interactions grow quickly in time as compared to short range explains for compensating distance with time. The dynamics of the spins (neurons) in terms of correlation function and structure factor at different time points has shown a perfect congruence with each other witnessing the universality in their behaviour as well as confirming the validity of dynamical scaling.
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