Krishnadas Mohandas, Krzysztof Suchecki, Janusz A Hołyst
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Paradise-disorder transition in structural balance dynamics on Erdös-Rényi graphs.
Structural balance has been posited as one of the factors influencing how friendly and hostile relations of social actors evolve over time. This study investigates the behavior of the Heider balance model in Erdös-Rényi random graphs in the presence of a noisy environment, particularly the transition from an initially entirely positively polarized paradise state to a disordered phase. We examine both single-layer and bilayer network configurations and provide a mean-field solution for the average link polarization that predicts a first-order transition where the critical temperature scales with the connection probability p as p^{2} for a monolayer system and in a more complex way for a bilayer. We show that, to mimic the dynamics observed in complete graphs, the intralayer Heider interaction strengths should be scaled as p^{-2}, while the interlayer interaction strengths should be scaled as p^{-1} for random graphs. Numerical simulations have been performed, and their results confirm our analytical predictions, provided that graphs are dense enough.
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.