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Related Experiment Video

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Modeling the Functional Network for Spatial Navigation in the Human Brain

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Annealing approximation in master-node network model.

M O Hase¹, Anderson A Ferreira², André C R Martins¹

¹University of São Paulo, School of Arts, Sciences, and Humanities, São Paulo, SP 03828-000, Brazil.

Physical Review. E

|January 21, 2026

Summary

This summary is machine-generated.

This study explores opinion dynamics using a master-node network model, revealing how asymmetric social influences (chirality) drive systems toward consensus or polarization via phase transitions.

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Area of Science:

Complex Systems
Statistical Physics
Social Dynamics

Background:

Opinion dynamics models often simplify social influence.
Understanding phase transitions is key to collective behavior.
Chirality (asymmetric influence) is an understudied factor in opinion formation.

Purpose of the Study:

To investigate absorbing-state phase transitions in opinion dynamics.
To analyze the role of chiral parameters (R and L) in network interactions.
To develop a theoretical framework for opinion convergence and divergence.

Main Methods:

Utilized a master-node network model.
Employed the annealing approximation for analysis.
Examined three fundamental regimes: disagreement, consensus, and mixed outcomes.

Main Results:

Identified continuous and discontinuous phase transitions between disordered and ordered phases.
Demonstrated that chiral parameters govern phase behavior.
Observed discontinuous transitions in systems with two absorbing states, dependent on initial conditions.

Conclusions:

Asymmetric social influences (chirality) are crucial symmetry-breaking elements in opinion formation.
The model explains how networks can lead to polarization or consensus.
Initial conditions critically influence the final state in systems with multiple absorbing states.