Heider balance on Archimedean lattices and cliques

Abstract

We investigate the work function $U(T)$ for the Heider balance, driven by a thermal noise $T$, on several planar networks that contain separated triangles, pairs of triangles, chains of triangles and complex structures of triangles. In simulations, the heat-bath algorithm is applied. Two schemes of link values updating are considered: synchronous and asynchronous (sequential). The latter results are compared with analytical calculations for small cliques. We argue that the actual shape of $U(T)$ is a consequence of a local topology rather than of a macroscopic ordering. Finally, we present the mathematical proof that for any planar lattice, perfect structural (Heider) balance is unreachable at $T>0$.

arXiv comment12 pages, 14 figures

References in corpus (22)

• Minority Opinion Spreading in Random Geometry
• Dynamics of Social Balance on Networks
• Balance in signed networks
• Statistical Physics of Balance Theory
• Mean-field solution of structural balance dynamics in nonzero temperature
• Phase transition in a network model of social balance with Glauber dynamics
• Testing structural balance theories in heterogeneous signed networks
• Quartic Balance Theory: Global Minimum With Imbalanced Triangles
• Towards the Heider balance with a cellular automaton
• Mean-Field Solution for Critical Behavior of Signed Networks in Competitive Balance Theory
• Heider and coevolutionary balance: From discrete to continuous phase transition
• Comment on `Phase transition in a network model of social balance with Glauber dynamics'
• Mean-field approximation for structural balance dynamics in heat-bath
• Heider balance of a chain of actors as dependent on the interaction range and a thermal noise
• Reply to "Comment on 'Phase transition in a network model of social balance with Glauber dynamics' "
• Towards the Heider balance -- a cellular automaton with a global neighborhood
• Hybrid balance theory: Heider balance under higher order interactions
• Thermal properties of structurally balanced systems on classical random graphs
• Thermal properties of structurally balanced systems on diluted and densified triangulations
• Expulsion from structurally balanced paradise
• Exact cluster dynamics of indirect reciprocity in complete graphs
• Modified Heider Balance on Sparse Random Networks