Droplet Finite-Size Scaling of the Majority Vote Model on Quenched Scale-Free Networks

2023/03/01 by Alencar, D. S. M., Alves, T. F. A., Lima, F. W. S. +3
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2303.00454

Abstract

We consider the Majority Vote model coupled with scale-free networks. Recent works point to a non-universal behavior of the Majority Vote model, where the critical exponents depend on the connectivity while the network's effective dimension D_eff is unity for a degree distribution exponent 5/2<γ<7/2. We present a finite-size theory of the Majority Vote Model for uncorrelated networks and present generalized scaling relations with good agreement with Monte-Carlo simulation results. The presented finite-size theory has two main sources of size dependence. The first source is an external field describing a mass media influence on the consensus formation and the second source is the scale-free network cutoff. The model indeed presents non-universal critical behavior where the critical exponents depend on the degree distribution exponent 5/2<γ<7/2. For γ≥ 7/2, the model is on the same universality class of the Majority Vote model on Erdös-Renyi random graphs, while for γ=7/2, the critical behavior presents additional logarithmic corrections.

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