Kinetic Continuous Opinion Dynamics Model on Two Types of Archimedean Lattices

Francisco W S Lima

doi:10.3389/fphy.2017.00047

Abstract

Here, the critical properties of kinetic continuous opinion dynamics model are studied on ($4,6,12$) and ($4,8^2$) Archimedean lattices. We obtain $p_c$ and the critical exponents from Monte Carlo simulations and finite size scaling. We found out the values of the critical points and Binder cumulant that are $p_c=0.086(3)$ and $O_4^*=0.59(2)$ for ($4,6,12$); and $p_c=0.109(3)$ and $O_4^*=0.606(5)$ for ($4,8^2$) lattices and also the exponent ratios $\beta/\nu$, $\gamma/\nu$ and $1/\nu$ are respectively: $0.23(7)$, $1.43(5)$ and $ 0.60(3)$ for ($4,6,12$); and $0.149(4)$, $1.56(4)$ and $0.94(4)$ for ($4,8^2$) lattices.

Highlights

In 1986 Galam introduced the use of local majority rules to study voting systems as bottomup democratic voting in hierarchical structures [1], see the references [2,3,4]
The results of the continuous version the kinetic continuous opinion dynamics (KCOD) model, obtained through numerical simulations indicate the existence of a universal continuous phase transition at p = pc with exponents of mean field (νd = 2.00(1), β = 0.50(1), and γ = 1.00(1))
We studied a non-equilibrium KCOD model through extensive Monte Carlo simulations on (4, 6, 12) and (4, 82) AL

Summary

INTRODUCTION

In 1986 Galam introduced the use of local majority rules to study voting systems as bottomup democratic voting in hierarchical structures [1], see the references [2,3,4]. The results of the continuous version the KCOD model, obtained through numerical simulations indicate the existence of a universal continuous phase transition at p = pc with exponents of mean field (νd = 2.00(1), β = 0.50(1), and γ = 1.00(1)). Similar to this KCOD model is the one of Deffuant et al [15], where each person i selects another person j to talk to (no lattice) and both move their opinion toward that of the other person. We compared our results with those of the MVM on (4, 6, 12) and (4, 82) [22]

DEFINITION AND SIMULATION

RESULTS AND DISCUSSION

CONCLUSION