Thermal properties of structurally balanced systems on diluted and densified triangulations

Abstract

The dynamics of social relations and the possibility of reaching the state of structural balance (Heider balance) are discussed for various networks of interacting actors under the influence of the temperature modeling the social noise level. For that purpose, two main types of lattices are considered. The first is created by removing some links from a regular triangular lattice to produce a diluted triangular lattice, and the second by adding more links to create an enhanced triangular lattice. In both those cases, the full range of possible graph densities is discussed, limited by the extreme cases of networks which consist of a small number of separated triads and fully connected networks. It is shown that the existence of the balanced state is not possible if the average node degree is too close to the value characterizing the regular triangular lattice. Otherwise, both balanced (or partially balanced) and imbalanced states are possible, depending on the temperature. However, only for graphs which are dense enough a phase transition of the first kind is observed, while less enhanced networks (and all diluted) indicate a smooth cross-over between the two states. The cross-over temperatures are size-independent only for the diluted triangular lattices and depend on the size of the system for the enhanced triangular lattices, as is the case also for the critical temperatures of the phase transition observed in denser enhanced lattices.

arXiv comment12 pages, 10 figures, RevTeX

References in corpus (15)

• Dynamics of Social Balance on Networks
• Nonequilibrium phase transition in the kinetic Ising model: Existence of tricritical point and stochastic resonance
• Statistical Physics of Balance Theory
• Mean-field solution of structural balance dynamics in nonzero temperature
• Homophily based on few attributes can impede structural balance
• Canonical local algorithms for spin systems: Heat Bath and Hasting's methods
• Phase transition in a network model of social balance with Glauber dynamics
• 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'
• 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' "
• Balanced-imbalanced transitions in indirect reciprocity dynamics on networks
• Expulsion from structurally balanced paradise

Cited by in corpus (6)

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• Thermal properties of structurally balanced systems on classical random graphs
• Exact cluster dynamics of indirect reciprocity in complete graphs
• Modified Heider Balance on Sparse Random Networks
• Indirect reciprocity as a dynamics for weak balance
• Heider balance on Archimedean lattices and cliques