Mean-field solution of structural balance dynamics in nonzero temperature.

Area of Science:

• Network Science
• Statistical Physics
• Sociophysics

Background:

• Signed networks exhibit a tendency towards structural balance, representing a state with minimal conflict.
• Real-world networks, however, often contain tensions despite this tendency.
• Existing models may not fully capture the dynamics of tension and balance.

Purpose of the Study:

• To generalize balance dynamics in signed networks to include nonzero temperatures.
• To model network tension tolerance using concepts from statistical physics.
• To investigate phase transitions in signed network structures.

Main Methods:

• Developed a dynamical model incorporating Boltzmann-Gibbs statistical physics.
• Assigned energy values to different triad configurations.
• Introduced temperature as a measure of network tension tolerance.
• Utilized mean-field analysis to solve the model.

Main Results:

• Identified a first-order phase transition from an imbalanced to a balanced state.
• Determined a critical temperature (T_{c}) above which the balanced state is unreachable.
• Observed a hysteresis loop associated with the phase transition, spanning balanced and imbalanced regimes.

Conclusions:

• The generalized model accurately reflects the interplay between tension and structural balance in signed networks.
• Temperature serves as a critical parameter influencing the network's ability to achieve balance.
• The findings provide insights into the dynamics of real-world social and interaction networks.