Annealing approximation in master-node network model

TL;DR

This paper uses annealing approximation to analyze phase transitions in opinion dynamics within a master-node network model, revealing how asymmetric influences lead to diverse collective behaviors.

Contribution

It introduces a theoretical framework for understanding opinion phase transitions considering asymmetric social influences and initial conditions.

Findings

Identification of phase diagram with continuous and discontinuous transitions

Discontinuous transitions depend on initial opinion distributions

Asymmetric influences drive polarization or consensus

Abstract

This paper investigates absorbing-state phase transitions in opinion dynamics through a master-node network model analyzed using annealing approximation. We develop a theoretical framework examining three fundamental regimes: systems converging to complete disagreement, complete consensus, or both states depending on initial conditions. The phase behavior is governed by two key chiral parameters: $R$ measuring right-oriented influence and $L$ measuring left-oriented influence in the network interactions. Our analysis reveals a rich phase diagram featuring both continuous and discontinuous transitions between disordered and ordered phases. The discontinuous transition emerges in systems with two absorbing states, where the final configuration depends critically on initial opinion distributions. The annealing approximation provides fundamental insights into how asymmetric social influences (chirality) shape collective opinion formation, acting as a symmetry-breaking element that drives the system toward polarization or consensus.