Consensus Formation In Continuous Opinion Dynamics On Quasiperiodic Lattices

We studied the Biswas-Chatterjee-Sen (BCS) consensus formation model, also known as the Kinetic Continuous Opinion Dynamics (KCOD) model on quasiperiodic lattices by using Kinetic Monte Carlo simulations and Finite Size Scaling technique. Our results are consistent with a continuous phase transition, controlled by an external noise. We obtained the order parameter M, defined as the averaged opinion, the fourth-order Binder cumulant U and susceptibility chi as functions of the noise parameter. We estimated the critical noises for Penrose and Ammann-Beenker lattices. We also considered seven-fold and nine-fold quasiperiodic lattices and estimated the respective critical noises as well. Irrespective of rotational and translational long-range order of the lattice, the system falls in the same universality class of the two-dimensional Ising model. Quasiperiodic order is irrelevant and it does not change any critical exponents for BCS model.