Three-State Majority-vote Model on Scale-Free Networks and the Unitary Relation for Critical Exponents

Abstract

We investigate the three-state majority-vote model for opinion dynamics on scale-free and regular networks. In this model, an individual selects an opinion equal to the opinion of the majority of its neighbors with probability 1 − q, and different to it with probability q. The parameter q is called the noise parameter of the model. We build a network of interactions where z neighbors are selected by each added site in the system, a preferential attachment network with degree distribution k−λ, where λ = 3 for a large number of nodes N. In this work, z is called the growth parameter. Using finite-size scaling analysis, we obtain that the critical exponents $$\beta /\bar{ u }$$ β / ν ¯ and $$\gamma /\bar{ u }$$ γ / ν ¯ associated with the magnetization and the susceptibility, respectively. Using Monte Carlo simulations, we calculate the critical noise parameter qc as a function of z for the scale-free networks and obtain the phase diagram of the model. We find that the critical exponents add up to unity when using a special volumetric scaling, regardless of the dimension of the network of interactions. We verify this result by obtaining the critical noise and the critical exponents for the two and three-state majority-vote model on cubic lattice networks.

Document Details

Document Type
Pub Defense Publication
Publication Date
May 19, 2020
Source ID
10.1038/s41598-020-63929-1

Entities

People

  • André L M Vilela
  • Bernardo J. Zubillaga
  • Chao Wang
  • H. Eugene Stanley
  • Minggang Wang
  • Ruijin Du

Organizations

  • ARPA-E
  • Defense Threat Reduction Agency
  • National Natural Science Foundation of China
  • National Science Foundation

Tags

Readers

  • Computational Modeling and Simulation
  • Neural Network Machine Learning.
  • Statistical inference.