Phase Transitions in Ising Model Defined on Complex Networks

Abstract

In this work, we consider an Ising model which allows spin-spin interaction in the systems. We assume that two-level quantum systems are randomly located in N nodes of a complex annealed scale-free network described by the Barabasi-Albert model. It is defined by the power-law degree distribution of nodes. We consider the mean-field approach to the system described by the Ising Hamiltonian. At a certain level, the system is totally characterized by the order parameter S_z. It contains a critical inverse temperature β, which depends on parameter ζ₂ as the ratio of the second to the first moment of the degree distribution. We have found that for ζ₂, that exceeds its critical value ζ_2,c, high temperature phase transition occurs that can be explained by the hubs and clusters which appear in scale-free networks.