Dinâmicas competitivas no modelo de Ising em uma rede complexa

Abstract

The Ising model on a complex network, both in thermodynamic equilibrium and out of equilibrium through competing dynamics, has been studied employing Monte Carlo simulations. The complex network in consideration follows a power-law degree distribution represented as p(k) ∼ k−α, where the minimum k0 and maximum km degree are xed for the entire network size, resulting in the so-called restricted scale-free network (RSFN). This new name comes from the fact that by restricting the degrees of the network, this is no longer a scale-free network, and we maintain the convergence of the second and fourth moments of the degree distribution. Consequently, critical points of the phase transition can be obtained, remaining nite for any value of α. The dynamics within the system can be determined by the probability parameter q. In this sense, q is the probability of the one-spin ip process act as dynamic of the system and simulates it in contact with a heat bath of temperature T. And with probability 1−q, the two-spin ip process mimics the system subjected to an external ux of energy into the system. In the case q = 1, representing the equilibrium model, thermodynamic quantities such as magnetization per spin mF N , susceptibility χN , and Binder cumulant UN have been calculated. Critical points of the system were obtained, allowing the construction of phases diagram of the temperature T as a function of k0, km and α. Furthermore, critical exponents of the system (β, γ, and ν) were determined using nite size scaling theory. In the case of the nonequilibrium model, featuring competing dynamics, in addition to the aforementioned quantities, antiferromagnetic magnetization mAF N was calculated. Critical points were determined as a function of q, leading to the construction of the phase diagram of the T as a function of q, in which we observed a self-organization phenomena in the ordered phases. By calculating the critical exponents of the system, we confirm that both the equilibrium and non-equilibrium models belong to the universality class of the mean eld approximation.