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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.

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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.