Critical properties of Heider balance on multiplex networks

TL;DR

This paper explores how Heider's balance theory behaves on multiplex networks, revealing complex phase transitions influenced by interlayer correlations and different initial configurations, with implications for understanding social dynamics.

Contribution

It introduces a multiplex network model combining Heider dynamics with Ising interlayer interactions, analyzing phase transitions and equilibrium states with analytical and simulation methods.

Findings

Discontinuous transition from paradise to disordered state with increasing temperature.

Higher critical temperature in multiplex networks compared to single-layer cases.

Additional phase transitions when one layer has a two-clique configuration.

Abstract

Heider's structural balance theory has proven invaluable in comprehending the dynamics of social groups characterized by both friendly and hostile relationships. Since people's relations are rarely single-faceted, we investigate Heider balance dynamics on a multiplex network, consisting of several copies of the same agent displaying correlated relations at different layers building the multiplex. Intralayer interactions in our model adhere to Heider dynamics, while interlayer correlations stem from Ising interactions, with the heat bath dynamics of link signs. The investigations uncover a multifaceted system with a diverse equilibrium landscape contingent on the coexistence of distinct phases across layers. We observe that starting from a paradise state with positive links in all layers, an increase in temperature triggers a discontinuous transition to a disordered state akin to single-layer scenarios. The critical temperature surpasses that of the single-layer case, a fact verified through extended mean-field analysis and agent-based simulations. Furthermore, the scenario shifts when one layer exhibits a two-clique configuration instead of a paradise state. This change introduces additional transitions: synchronization of inter-layer relations and a transition to the disorder, appearing at a different, lower temperature compared to matching paradise states. This exploration shows the intricate interplay of Heider balance and multiplex interactions.