Droplet finite-size scaling of the majority-vote model on scale-free networks.

We discuss the majority vote model coupled with scale-free networks and investigate its critical behavior. Previous studies point to a nonuniversal behavior of the majority vote model, where the critical exponents depend on the connectivity. At the same time, the effective dimension D_{eff} is unity for a degree distribution exponent 5/2<γ<7/2. We introduce 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. Our finite-size approach has two sources of size dependence: an external field representing the influence of the mass media on consensus formation and the scale-free network cutoff. The critical exponents are nonuniversal, dependent on the degree distribution exponent, precisely when 5/2<γ<7/2. For γ≥7/2, the model is in the same universality class as the majority vote model on Erdos-Rényi random graphs. However, for γ=7/2, the critical behavior includes additional logarithmic corrections.

Diffusive majority-vote model.

We define a stochastic reaction-diffusion process that describes a consensus formation in a nonsedentary population. The process is a diffusive version of the majority-vote model, where the state update follows two stages: In the first stage, spins are allowed to jump to a random neighbor node with probabilities D_{+} and D_{-} for the respective spin orientations, and in the second stage, the spins in the same node can change its values according to the majority-vote update rule. The model presents a consensus formation phase when the concentration is greater than a threshold value and a paramagnetic phase on the converse for equal diffusion probabilities, i.e., maintaining the inversion symmetry. Setting unequal diffusion probabilities for the respective spin orientations is the same as applying an external magnetic field. The system undergoes a discontinuous phase transition for concentrations higher than the critical threshold on the external field. The individuals that diffuse more dominate the stationary collective opinion.

Erratum: Critical properties of a two-dimensional Ising magnet with quasiperiodic interactions [Phys. Rev. E 93, 042111 (2016)].

This corrects the article DOI: 10.1103/PhysRevE.93.042111.

Erratum: Critical properties of a two-dimensional Ising magnet with quasiperiodic interactions [Phys. Rev. E 93, 042111 (2016)].

This corrects the article DOI: 10.1103/PhysRevE.93.042111.

Critical properties of a two-dimensional Ising magnet with quasiperiodic interactions.

We address the study of quasiperiodic interactions on a square lattice by using an Ising model with ferromagnetic and antiferromagnetic exchange interactions following a quasiperiodic Fibonacci sequence in both directions of a square lattice. We applied the Monte Carlo method, together with the Metropolis algorithm, to calculate the thermodynamic quantities of the system. We obtained the Edwards-Anderson order parameter q_{EA}, the magnetic susceptibility χ, and the specific heat c in order to characterize the universality class of the phase transition. We also use the finite size scaling method to obtain the critical temperature of the system and the critical exponents ß,γ, and ν. In the low-temperature limit we obtained a spin-glass phase with critical temperature around T_{c}≈2.274, and the critical exponents ß,γ, and ν, indicating that the quasiperiodic order induces a change in the universality class of the system. Also, we discovered a spin-glass ordering in a two-dimensional system which is rare and, as far as we know, the unique example is an under-frustrated Ising model.