Disordered configurations of the Glauber model on two-dimensional networks (Vol. 49, No. 3)

A disordered configuration with two domains comprises a multiclustered state on the lattice.

The Glauber model provides a paradigm for modeling ordering processes in complex systems. The question that we answer is: How is the efficiency of the ordering process in the Glauber model affected if we rewire the links of the two-dimensional host lattice? Our research reveals that the fraction of disordered configurations exhibits a nonlinear dependence on the rewiring probability. In the small-world regime, the Glauber dynamics remains trapped in a metastable configuration that is disordered. In fact, we have observed a stationary state that consists of two intertwined domains of similar size, as shown in the figure. For higher rewiring probabilities, we observe isolated droplets of spins, which emerge due to poorly connected nodes in the network. We have also studied what happens to the ordering process on two-layer networks, in particular comparing outcomes on a multiplex network and on the corresponding network with random inter-layer connections. We have shown that, in this case, the properties of the stationary state are strongly affected by the type of inter-layer connections.

I. Baĉić, I. Franović and M. Perc , Disordered configurations of the Glauber model in two-dimensional networks, EPL, 120, 68001 (2017)