Regensburg 2025 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 26: Networks, From Topology to Dynamics (joint session SOE/BP/DY)
DY 26.2: Talk
Wednesday, March 19, 2025, 15:15–15:30, H45
Critical properties of Heider balance on multiplex networks — •Krishnadas Mohandas, Krzysztof Suchecki, and Janusz Hołyst — Faculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland
Heider’s structural balance theory has proven invaluable in comprehending the dynamics of social groups characterized by both friendly and hostile relationships. Extending this understanding to multiplex networks, we investigate Heider balance dynamics in systems where agents exhibit correlated relations across multiple layers. In our model, intralayer interactions adhere to Heider dynamics, while interlayer correlations are governed by Ising interactions, using heat bath dynamics for link signs. This framework reveals a multifaceted equilibrium landscape, with distinct phases coexisting across layers. Starting from a paradise state with positive links in all layers, increasing temperature induces a discontinuous transition to disorder, similar to single-layer scenarios but with a higher critical temperature, as verified through extended mean-field analysis and agent-based simulations.
We extend this analysis to Erdös-Rényi random graphs in noisy environments. We predict a first-order transition with a critical temperature scaling as p2 for monolayers and follow a more complex behavior for bilayers. To replicate dynamics observed in complete graphs, intralayer Heider interaction strengths must scale as p−2, while interlayer interaction strengths scale as p−1 in random graphs. Numerical simulations confirm these analytical predictions for dense graphs.
Keywords: Mean field theory; Multilayer & multiplex networks; Random graphs; Phase transitions; Metropolis algorithm