Ising Model In Networks Research Articles

Double phase transition of the Ising model in core–periphery networks

We study the phase transition of the Ising model in networks with core–periphery structures. By Monte Carlo simulations, we show that prior to the order-disorder phase transition the system organizes into an inhomogeneous intermediate phase in which core nodes are much more ordered than peripheral nodes. Interestingly, the susceptibility shows double peaks at two distinct temperatures. We find that, if the connections between core and periphery increase linearly with network size, the first peak does not exhibit any size-dependent effect, and the second one diverges in the limit of infinite network size. Otherwise, if the connections between the core and periphery scale sub-linearly with the network size, both peaks of the susceptibility diverge as power laws in the thermodynamic limit. This suggests the appearance of a double transition phenomenon in the Ising model for the latter case. Moreover, we develop a mean-field theory that agrees well with the simulations.

Opinion formation on the social networks with geographic structure

Opinion formation is the result of co-evolution of individual behavior and environment. Individual behavior is determined by its rational cognition and irrational emotion. Environment includes culture, cognitive and behavioral patterns and social interactions. Culture and cognitive patterns are usually related to the spatial factors. In this paper, a social network with geographical factors is constructed. Together with the Ising model in networks, the effects of both spatial and social factors on opinion formation are investigated. The phase transition in the process of opinion formation is studied. The results indicate that both spatial cultural background and global preference for public opinion are crucial to opinion formation.