CSH Talk by Janusz Holyst: “Phase transitions in coupled networks”

Modular structure of networks significantly increases complexity of phase transitions scenarios and it especially interesting when we simulate opinions in coupled social groups. In cases of Ising-like and majority dynamics phases of opposite values of order parameter (group opinions) can coexist at connected complex networks if the coupling strength between communities is below a critical threshold. When the number of interlinks increases a discontinuous phase transition takes place and values of the order parameter in both networks are the same. A similar effect can be observed when one increases the system temperature instead the internetwork couplings. When the network topology is not static, i.e . links and sites coevolve and a node can rewire its link to another node of the same state with probability p then an absorbing transition to a frozen phase above a critical value of rewiring probability takes place. In such a case the social group is split to two communities with no interlinks. Our analytical and numerical studies show that in the active phase mean values of magnetization of nodes and links tend to the same value that depends on initial conditions. I will consider also the problem of Heider balance in a link multiplex, i.e. a special multiplex where coupling exists only between corresponding links. Numerical simulations and analytical calculations demonstrate that the presence of such interlayer connections hinders the emergence of the Heider balance.

Results will be illustrated by on-line numerical simulations of opinion dynamics in coupled communities.

Ref.
1. K. Suchecki and J.A. Hołyst, Bistable-monostable transition in the Ising model on two connected complex networks , Physical Review E 80, 031110 (2009)
2. R. Lambiotte, M. Ausloos, Janusz A. Hołyst, Majority model on a network with communities
Physical Review E 75, 030101 (2007).
3. J Toruniewska, K Kułakowski, K Suchecki, JA Hołyst, Coupling of link-and node-ordering in the coevolving voter model, Physical Review E 96, 042306 (2017)
4. PJ Górski, K Kułakowski, P Gawroński, JA Hołyst, Destructive influence of interlayer coupling on Heider balance in bilayer networks, Scientific Reports 7, 16047 (2017)