Bistable-monostable transition in the Ising model on two connected complex networks.

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.