BCS model on Quasiperiodic Lattices

TL;DR

This study investigates the BCS opinion dynamics model on quasiperiodic lattices, finding that the phase transition behavior aligns with the 2D Ising universality class regardless of lattice order.

Contribution

It demonstrates that quasiperiodic order does not affect the critical behavior of the BCS model, extending understanding of phase transitions on complex lattices.

Findings

Identified critical noise values for various quasiperiodic lattices.

Confirmed the universality class matches the 2D Ising model.

Showed quasiperiodic order does not alter critical exponents.

Abstract

We study the Biswas-Chatterjee-Sen (BCS) model, also known as the KCOD (Kinetic Continuous Opinion Dynamics) 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 7-fold and 9-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.