The KCOD Model on (3,4,6,4) and (34,6) Archimedean Lattices

Francisco De Sousa Lima

doi:10.3390/e19090459

Abstract

Through Monte Carlo simulations, we studied the critical properties of kinetic models of continuous opinion dynamics on ( 3 , 4 , 6 , 4 ) and ( 3 4 , 6 ) Archimedean lattices. We obtain p c and the critical exponents’ ratio from extensive Monte Carlo studies and finite size scaling. The calculated values of the critical points and Binder cumulant are p c = 0 . 085 ( 6 ) and O 4 * = 0 . 605 ( 9 ) ; and p c = 0 . 146 ( 5 ) and O 4 * = 0 . 606 ( 3 ) for ( 3 , 4 , 6 , 4 ) and ( 3 4 , 6 ) lattices, respectively, while the exponent ratios β / ν , γ / ν and 1 / ν are, respectively: 0 . 126 ( 1 ) , 1 . 50 ( 7 ) , and 0 . 90 ( 5 ) for ( 3 , 4 , 6 , 4 ); and 0 . 125 ( 3 ) , 1 . 54 ( 6 ) , and 0 . 99 ( 3 ) for ( 3 4 , 6 ) lattices. Our new results agree with majority-vote model on previously studied regular lattices and disagree with the Ising model on square-lattice.

Highlights

IntroductionThe study of the behavior of individuals in a society by physicists is known as sociophysics, having as the main contributor in this new research area Serge Galam who introduced the use of local majority rules to study voting systems as bottom-up democratic voting in hierarchical structures [1,2,3,4]
Through Monte Carlo simulations, we studied the critical properties of kinetic models of continuous opinion dynamics on (3, 4, 6, 4) and (34, 6) Archimedean lattices
We studied a nonequilibrium KCOD model through extensive Monte Carlo simulations on

Summary

Introduction

The study of the behavior of individuals in a society by physicists is known as sociophysics, having as the main contributor in this new research area Serge Galam who introduced the use of local majority rules to study voting systems as bottom-up democratic voting in hierarchical structures [1,2,3,4]. Sociophysics was rejected by some physicists in the eighties [5], it has today become an active field of research among physicists all over the world [3,6,7] In this same context and based on the criterion of Grinstein et al [8] (where a nonequilibrium model presenting up–down symmetry in two-state dynamic systems implies the same critical behavior (same universality class) as the equilibrium Ising model), Oliveira [9] proposed a nonequilibrium version of Ising model called majority vote model (MVM). Lima and Malarz [14] studied the MVM on (3, 4, 6, 4) and (34 , 6) Archimedean lattices (ALs) On these lattices, they found a second-order phase transition with exponent ratios β/ν = 0.103(6), γ/ν = 1.596(54), 1/ν = 0.872(85) for (3, 4, 6, 4) and β/ν = 0.114(3), γ/ν = 1.632(35), 1/ν = 0.98(10). We compared our results with those of the MVM made on (3, 4, 6, 4) and (34 , 6) AL

Model and Simulations

Results and Discussion

Conclusions