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تسجيل مستخدم جديدExplosive Phase Transition in a Majority-Vote Model with Inertia
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We generalize the original majority-vote model by incorporating an inertia into the microscopic dynamics of the spin flipping, where the spin-flip probability of any individual depends not only on the states of its neighbors, but also on its own state. Surprisingly, the order-disorder phase transition is changed from a usual continuous type to a discontinuous or an explosive one when the inertia is above an appropriate level. A central feature of such an explosive transition is a strong hysteresis behavior as noise intensity goes forward and backward. Within the hysteresis region, a disordered phase and two symmetric ordered phases are coexisting and transition rates between these phases are numerically calculated by a rare-event sampling method. A mean-field theory is developed to analytically reveal the property of this phase transition.
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We study a nonequilibrium model with up-down symmetry and a noise parameter $q$ known as majority-vote model of M.J. Oliveira 1992 with heterogeneous agents on square lattice. By Monte Carlo simulations and finite-size scaling relations the critical
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The dynamics of opinion formation in a society is a complex phenomenon where many variables play an important role. Recently, the influence of algorithms to filter which content is fed to social networks users has come under scrutiny. Supposedly, the
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The majority-vote model with noise is one of the simplest nonequilibrium statistical model that has been extensively studied in the context of complex networks. However, the relationship between the critical noise where the order-disorder phase trans
ition takes place and the topology of the underlying networks is still lacking. In the paper, we use the heterogeneous mean-field theory to derive the rate equation for governing the models dynamics that can analytically determine the critical noise $f_c$ in the limit of infinite network size $Nrightarrow infty$. The result shows that $f_c$ depends on the ratio of ${leftlangle k rightrangle }$ to ${leftlangle k^{3/2} rightrangle }$, where ${leftlangle k rightrangle }$ and ${leftlangle k^{3/2} rightrangle }$ are the average degree and the $3/2$ order moment of degree distribution, respectively. Furthermore, we consider the finite size effect where the stochastic fluctuation should be involved. To the end, we derive the Langevin equation and obtain the potential of the corresponding Fokker-Planck equation. This allows us to calculate the effective critical noise $f_c(N)$ at which the susceptibility is maximal in finite size networks. We find that the $f_c-f_c(N)$ decays with $N$ in a power-law way and vanishes for $Nrightarrow infty$. All the theoretical results are confirmed by performing the extensive Monte Carlo simulations in random $k$-regular networks, Erdos-Renyi random networks and scale-free networks.
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