Abstract
In this paper, we investigate the behavior of the Ising model on two sparsely connected complex networks. The networks have the topology of a random graph or Barabási and Albert scale-free networks. We extend our previous analysis and show that a bistable-monostable phase transition occurs in such systems. During this transition, the magnetization undergoes a discontinuous jump. We calculate the critical temperature analytically for regular random graphs and study a more general case using an iterative map corresponding to mean-field dynamics. The calculations are confirmed by numeric simulations based on Monte Carlo approach.
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