Heider and coevolutionary balance: From discrete to continuous phase transition

Abstract

Structural balance in social complex networks has been modeled with two types of triplet interactions. First, the interaction that only considers dynamic role for links or relationships (Heider balance), and second, the interaction that considers both individual opinions (nodes) and relationships in network dynamics (coevolutionary balance). The question is, as the temperature varies, which is a measure of social disorder, how structural balance can be created or destroyed by each of these triplet interactions? We use statistical mechanics methods and observe through analytical calculation and numerical simulation that unlike the Heider balance triplet interaction which has a discrete phase transition, the coevolutionary balance has a continuous phase transition. The critical temperature of the presented model change with the root square of network size which is a linear dependence in thermal Heider balance.

arXiv comment7 pages, 6 figures

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Cited by in corpus (6)

• Hybrid balance theory: Heider balance under higher order interactions
• Second to first order phase transition; coevolutionary versus structural balance
• Thermal properties of structurally balanced systems on classical random graphs
• Pseudo-Phase Transitions of Ising and Baxter-Wu Models in Two-Dimensional Finite-Size Lattices
• Thermal properties of structurally balanced systems on diluted and densified triangulations
• Heider balance on Archimedean lattices and cliques