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

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 probabilityq. The parameterqis called the noise parameter of the model. We build a network of interactions wherezneighbors are selected by each added site in the system, a preferential attachment network with degree distributionkλ, whereλ = 3 for a large number of nodesN. In this work,zis called the growth parameter. Using finite-size scaling analysis, we obtain that the critical exponents$$\beta /\bar{\nu }$$β/ν¯and$$\gamma /\bar{\nu }$$γ/ν¯associated with the magnetization and the susceptibility, respectively. Using Monte Carlo simulations, we calculate the critical noise parameterqcas a function ofzfor 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.

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Publication Date:
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Scientific Reports
Nature Publishing Group
Sponsoring Org:
National Science Foundation
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