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