Three-state Voter Model on Barab\'asi-Albert Networks and the Unitary Relation for Critical Exponents

We investigate the three-state majority-vote model with noise on scale-free networks. In this model, an individual selects an opinion equal to the opinion of the majority of its neighbors with probability 1 - q and opposite to it with probability q. We build a network of interactions where z neighbors are selected by each added site in the system, yielding a preferential attachment network with degree distribution k^-λ, where λ ∼ 3. Using Q finite-size scaling for any dimensions and the finite-size scaling for complex networks, we show that the critical exponents associated to the magnetization and to the susceptibility are related by 2β/ν + γ/ν = 1, regardless the dimension of the complex network. Using Monte Carlo simulations we obtain the phase diagram of the model and we verify the unitary relation for the critical exponents numerically by calculating β/ν, γ/ν and 1/ν for several values of the parameter z.