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Networks that have power-law connectivity, commonly referred to as the scale-free networks, are an important class of complex networks. A heterogeneous mean-field approximation has been previously proposed for the Ising model of the Barab{a}si-Albert model of scale-free networks with classical spins on the nodes wherein it was shown that the critical temperature for such a system scales logarithmically with network size. For finite sizes, there is no criticality for such a system and hence no true phase transition in terms of singular behavior. Further, in the thermodynamic limit, the mean-field prediction of an infinite critical temperature for the system may exclude any true phase transition even then. Nevertheless, with an eye on potential applications of the model on biological systems that are generally finite, one may still try to find approximations that describe the relevant observables quantitatively. Here we present an alternative, approximate formulation for the description of the Ising model of a Barab{a}si-Albert Network. Using the classical definition of magnetization, we show that Ising models on a network can be well-approximated by a long-range interacting homogeneous Ising model wherein each node of the network couples to all other spins with a strength determined by the mean degree of the Barab{a}si-Albert Network. In such an effective long-range Ising model of a Barab{a}si-Albert Network, the critical temperature is directly proportional to the number of preferentially attached links added to grow the network. The proposed model describes the magnetization of the majority of the sites with average or smaller than average degree better compared to the heterogeneous mean-field approximation. The long-range Ising model is the only homogeneous description of Barab{a}si-Albert networks that we know of.
With up to 7 million spins, the existence of spontaneous magnetization of Ising spins on directed Barabasi-Albert networks is investigated by Monte Carlo simulations. We confirm our earlier result that the magnetization for different temperatures T d
The existence of spontaneous magnetization of Ising spins on directed Barabasi-Albert networks is investigated with seven neighbors, by using Monte Carlo simulations. In large systems we see the magnetization for different temperatures T to decay aft
We investigate the behavior of the Ising model on two connected Barabasi-Albert scale-free networks. We extend previous analysis and show that a first order temperature-driven phase transition occurs in such system. The transition between antiparalel
We check the existence of a spontaneous magnetisation of Ising and Potts spins on semi-directed Barabasi-Albert networks by Monte Carlo simulations. We verified that the magnetisation for different temperatures $T$ decays after a characteristic time
We study critical behavior of the diluted 2D Ising model in the presence of disorder correlations which decay algebraically with distance as $sim r^{-a}$. Mapping the problem onto 2D Dirac fermions with correlated disorder we calculate the critical p