Quartic balance theory: Global minimum with imbalanced triangles.

Area of Science:

• Social network analysis
• Statistical physics
• Psychological modeling

Background:

• Heider's balance theory models triplet interactions in signed networks.
• The theory assumes triad independence, leading to perfectly balanced network states.
• Real-world networks often exhibit partial balance, indicating limitations in existing models.

Purpose of the Study:

• To investigate mechanisms preventing perfect balance in social networks.
• To propose and analyze a model with quartic interactions that dissolves triad independence.
• To understand the emergence of stable, partially imbalanced network states.

Main Methods:

• Development of a social network model incorporating quartic interactions.
• Application of the mean-field method to study system thermodynamics.
• Analysis of thermal behavior with temperature as a stochasticity parameter.

Main Results:

• A discrete phase transition occurs at a critical temperature, breaking symmetry between balanced and imbalanced triads.
• The model predicts two new stable states where either balanced or imbalanced triads dominate.
• Critical temperature dependence on the number of nodes is quadratic, differing from linear dependence in prior theories.

Conclusions:

• Quartic interactions can explain the prevalence of partial balance in real social networks.
• The model provides a theoretical framework for understanding emergent stability in complex social systems.
• Simulations validate the mean-field predictions, supporting the proposed mechanism.