Nonequilibrium system on a restricted scale-free network

The nonequilibrium Ising model on a restricted scale-free network has been studied with one- and two-spin flip competing dynamics employing Monte Carlo simulations. The dynamics present in the system can be defined by the probability q in which the one-spin flip process simulate the contact with a heat bath at a given temperature T, and with a probability (1−q) the two-spin flip process mimics the system subjected to an external flux of energy into it. The system network is described by a power-law degree distribution in the form P(k)∼k−α, and the restriction is made by fixing the maximum, km, and minimum, k0, degree on distribution for the whole network size. This restriction keeps finite the second and fourth moment of degree distribution, allowing us to obtain a finite critical point for any value of α. For these critical points, we have calculated the thermodynamic quantities of the system, such as, the total mNF and staggered mNAF magnetizations per spin, susceptibility χN, and reduced fourth-order Binder cumulant UN, for several values of lattice size N and exponent 1≤α≤5. Therefore, the phase diagram was built and a self-organization phenomena is observed from the transitions between antiferromagnetic AF to paramagnetic P, and P to ferromagnetic F phases. Using the finite-size scaling theory, we also obtained the critical exponents for the system, and a mean-field critical behavior is observed, exhibiting the same universality class of the system on the equilibrium and out of it.