Modified Heider balance on Erdös-Rényi networks
R Masoumi1, F Oloomi1, S Sajjadi2,3
1Department of Physics, Shahid Beheshti University, Evin, Tehran 19839, Iran.
Physical Review. E
|October 21, 2022
Summary
This study explores structural balance on random networks, revealing a first-order phase transition with temperature and hysteresis. Network connectivity influences transition temperatures and hysteresis loop width.
Area of Science:
- Statistical physics
- Network science
- Computational social science
Background:
- Standard balance models lack signed random networks, limiting analysis of underlying dynamics.
- Original balance models do not preserve tensed triads, necessitating extensions for comprehensive study.
- Recent work investigated balance models on fully connected signed networks, showing abrupt phase transitions.
Purpose of the Study:
- To examine the thermal behavior of the structural balance model on Erdös-Rényi random networks.
- To investigate the impact of network connectivity on phase transitions and hysteresis.
- To provide a mean-field solution and validate with simulations.
Main Methods:
- Defining the structural balance model on Erdös-Rényi random networks.
- Developing a mean-field solution to analyze thermal behavior.
- Conducting Monte Carlo simulations for result validation.
Main Results:
- A first-order phase transition with temperature was observed across various connection probabilities.
- Two transition temperatures, T_{cold} and T_{hot}, were identified, defining a hysteresis loop.
- Decreasing connection probability narrows the hysteresis loop, which disappears at a critical point.
Conclusions:
- The structural balance model on random networks exhibits a temperature-driven first-order phase transition with hysteresis.
- Network connectivity critically affects the transition temperatures and the extent of the metastable region.
- Mean-field predictions are supported by Monte Carlo simulations, providing a robust understanding of the model's behavior.
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