Nonequilibrium opinion dynamics on triangular, honeycomb, and Kagome lattices

2017 ◽  
Vol 28 (10) ◽  
pp. 1750123 ◽  
Author(s):  
F. W. S. Lima ◽  
N. Crokidakis
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Ising Model ◽  
Critical Exponents ◽  
Majority Vote ◽  
Opinion Dynamics ◽  
Dynamics Model ◽  
Vote Model ◽  
Disorder Phase Transition ◽  
Disorder Parameter

The Ising model on all Archimedean lattices exhibits spontaneous ordering. Three examples of these lattices, namely triangular ([Formula: see text]), honeycomb [Formula: see text] and Kagome [Formula: see text] lattices, are considered to study the kinetic continuous opinion dynamics model (KCOD) through extensive Monte Carlo simulations. The order/disorder phase transition is observed in all lattices for the KCOD. The estimated values of the critical disorder parameter are [Formula: see text], [Formula: see text], and [Formula: see text] for [Formula: see text], [Formula: see text] and [Formula: see text] lattices, respectively. The critical exponents [Formula: see text], [Formula: see text] and [Formula: see text] for the model are [Formula: see text], [Formula: see text], and [Formula: see text]; [Formula: see text], [Formula: see text], and [Formula: see text]; [Formula: see text], [Formula: see text], and [Formula: see text], for [Formula: see text], [Formula: see text] and [Formula: see text] lattices, respectively. These results agree with the majority-vote model on ([Formula: see text]), ([Formula: see text]), and [Formula: see text] lattices but are different from KCOD model results on square lattices [Formula: see text].

scholarly journals MAJORITY-VOTE MODEL ON (3, 4, 6, 4) AND (34, 6) ARCHIMEDEAN LATTICES

2006 ◽  
Vol 17 (09) ◽  
pp. 1273-1283 ◽  
Author(s):  
F. W. S. LIMA ◽  
K. MALARZ
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Critical Exponents ◽  
Majority Vote ◽  
Embedding Dimension ◽  
Vote Model ◽  
Disorder Phase Transition ◽  
Regular Lattices

On Archimedean lattices, the Ising model exhibits spontaneous ordering. Two examples of these lattices of the majority-vote model with noise are considered and studied through extensive Monte Carlo simulations. The order/disorder phase transition is observed in this system. The calculated values of the critical noise parameter are qc = 0.091(2) and qc = 0.134(3) for (3, 4, 6, 4) and (34, 6) Archimedean lattices, respectively. The critical exponents β/ν, γ/ν and 1/ν for this model are 0.103 (6), 1.596 (54), 0.872 (85) for (3, 4, 6, 4) and 0.114 (3), 1.632 (35), 0.98 (10) for (34, 6) Archimedean lattices. These results differs from the usual Ising model results and the majority-vote model on so-far studied regular lattices or complex networks. The effective dimensionalities of the system [D eff (3, 4, 6, 4) = 1.802(55) and D eff (34, 6) = 1.860(34)] for these networks are reasonably close to the embedding dimension two.

scholarly journals MAJORITY-VOTE ON DIRECTED SMALL-WORLD NETWORKS

2007 ◽  
Vol 18 (08) ◽  
pp. 1251-1261 ◽  
Author(s):  
EDINA M. S. LUZ ◽  
F. W. S. LIMA
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Critical Exponents ◽  
Order Parameter ◽  
Majority Vote ◽  
Small World ◽  
Small World Network ◽  
Small World Networks ◽  
Vote Model ◽  
Disorder Phase Transition

On directed small-world networks the majority-vote model with noise is now studied through Monte Carlo simulations. In this model, the order-disorder phase transition of the order parameter is well defined. We calculate the value of the critical noise parameter qc for several values of rewiring probability p of the directed small-world network. The critical exponents β/ν, γ/ν and 1/ν were calculated for several values of p.

scholarly journals MAJORITY-VOTE ON DIRECTED BARABÁSI–ALBERT NETWORKS

2006 ◽  
Vol 17 (09) ◽  
pp. 1257-1265 ◽  
Author(s):  
F. W. S. LIMA
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Decay Time ◽  
Order Parameter ◽  
Majority Vote ◽  
Arrhenius Law ◽  
Vote Model ◽  
Disorder Phase Transition

On directed Barabási–Albert networks with two and seven neighbours selected by each added site, the Ising model was seen not to show a spontaneous magnetisation. Instead, the decay time for flipping of the magnetisation followed an Arrhenius law for Metropolis and Glauber algorithms, but for Wolff cluster flipping the magnetisation decayed exponentially with time. On these networks the Majority-vote model with noise is now studied through Monte Carlo simulations. However, in this model, the order-disorder phase transition of the order parameter is well defined in this system. We calculate the value of the critical noise parameter qc for several values of connectivity z of the directed Barabási–Albert network. The critical exponentes β/ν, γ/ν and 1/ν were calculated for several values of z.

scholarly journals TAX EVASION AND NONEQUILIBRIUM MODEL ON APOLLONIAN NETWORKS

2012 ◽  
Vol 23 (11) ◽  
pp. 1250079 ◽  
Author(s):  
F. W. S. LIMA
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Critical Temperature ◽  
Ising Model ◽  
Tax Evasion ◽  
Majority Vote ◽  
Vote Model ◽  
Agent Based ◽  
Equilibrium Dynamics ◽  
Economics Model

The Zaklan model had been proposed and studied recently using the equilibrium Ising model on square lattices (SLs) by [G. Zaklan, F. Westerhoff and D. Stauffer, J. Econ. Interact. Coord.4, 1 (2008), arXiv:0801.2980; G. Zaklan, F. W. S. Lima and F. Westerhoff, Physica A387, 5857 (2008)], near the critical temperature of the Ising model presenting a well-defined phase transition; but on normal and modified Apollonian networks (ANs), [J. S. Andrade, Jr., H. J. Herrmann, R. F. S. Andrade, and L. R. da Silva, Phys. Rev. Lett.94, 018702 (2005); R. F. S. Andrade, J. S. Andrade Jr. and H. J. Herrmann, Phys. Rev. E79, 036105 (2009)] studied the equilibrium Ising model. They showed the equilibrium Ising model not to present on ANs a phase transition of the type for the 2D Ising model. Here, using agent-based Monte Carlo simulations, we study the Zaklan model with the well-known majority-vote model (MVM) with noise and apply it to tax evasion on ANs, to show that differently from the Ising model the MVM on ANs presents a well-defined phase transition. To control the tax evasion in the economics model proposed by Zaklan et al., MVM is applied in the neighborhood of the critical noise qc to the Zaklan model. Here we show that the Zaklan model is robust because this can also be studied, besides using equilibrium dynamics of Ising model, through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.

scholarly journals Kinetic Models of Discrete Opinion Dynamics on Directed Barabási–Albert Networks

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 942 ◽  
Author(s):  
F. Welington S. Lima ◽  
J. A. Plascak
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Kinetic Models ◽  
Order Parameter ◽  
Majority Vote ◽  
Opinion Dynamics ◽  
Universality Class ◽  
Continuous Phase ◽  
Vote Model ◽  
Continuous Phase Transition

Kinetic models of discrete opinion dynamics are studied on directed Barabási–Albert networks by using extensive Monte Carlo simulations. A continuous phase transition has been found in this system. The critical values of the noise parameter are obtained for several values of the connectivity of these directed networks. In addition, the ratio of the critical exponents of the order parameter and the corresponding susceptibility to the correlation length have also been computed. It is noticed that the kinetic model and the majority-vote model on these directed Barabási–Albert networks are in the same universality class.

scholarly journals ISING MODEL SPIN S = 1 ON DIRECTED BARABÁSI–ALBERT NETWORKS

2006 ◽  
Vol 17 (09) ◽  
pp. 1267-1272 ◽  
Author(s):  
F. W. S. LIMA
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Ising Model ◽  
Order Phase Transition ◽  
Decay Time ◽  
Arrhenius Law ◽  
Disorder Phase Transition ◽  
First Order ◽  
First Order Phase Transition ◽  
First Order Phase

On directed Barabási–Albert networks with two and seven neighbours selected by each added site, the Ising model with spin S = 1/2 was seen not to show a spontaneous magnetisation. Instead, the decay time for flipping of the magnetisation followed an Arrhenius law for Metropolis and Glauber algorithms, but for Wolff cluster flipping the magnetisation decayed exponentially with time. On these networks the Ising model spin S = 1 is now studied through Monte Carlo simulations. However, in this model, the order-disorder phase transition is well defined in this system. We have obtained a first-order phase transition for values of connectivity m = 2 and m = 7 of the directed Barabási–Albert network.

Critical exponents and the universality class of a minesweeper percolation model

2020 ◽  
Vol 31 (09) ◽  
pp. 2050129
Author(s):  
Yuqi Qing ◽  
Wen-Long You ◽  
Maoxin Liu
Keyword(s):  
Phase Transition ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Critical Exponents ◽  
Critical Density ◽  
Universality Class ◽  
Percolation Model ◽  
System Configuration ◽  
Percolation Transition ◽  
Second Order Phase Transition

We introduce a minesweeper percolation model, in which the system configuration is obtained via an automatic minesweeper process. For a variety of candidate networks with different lattice configurations, our process gives rise to a second-order phase transition. Using Monte Carlo simulation, we identify the critical points implied by giant components. A set of critical exponents are extracted to characterize the nature of the minesweeper percolation transition. The determined universality class shows a clear difference from the traditional percolation transition. A proper mine density of the minesweeper game should be set around the critical density.

scholarly journals Short-time Monte Carlo simulation of the majority-vote model on cubic lattices

2021 ◽  
Vol 574 ◽  
pp. 125973
Author(s):  
K.P. do Nascimento ◽  
L.C. de Souza ◽  
A.J.F. de Souza ◽  
André L.M. Vilela ◽  
H. Eugene Stanley
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Majority Vote ◽  
Vote Model ◽  
Cubic Lattices ◽  
Short Time

Majority-vote model on directed Small-World-Voronoi–Delaunay random lattices

2018 ◽  
Vol 29 (07) ◽  
pp. 1850061
Author(s):  
R. S. C. Brenda ◽  
F. W. S. Lima
Keyword(s):  
Critical Exponents ◽  
Majority Vote ◽  
Small World ◽  
Universality Class ◽  
Two Dimensions ◽  
Critical Properties ◽  
Disordered System ◽  
Vote Model ◽  
Random Lattices ◽  
Second Order Phase Transition

We investigate the critical properties of the nonequilibrium majority-vote model in two-dimensions on directed small-world lattice with quenched connectivity disorder. The disordered system is studied through Monte Carlo simulations: the critical noise ([Formula: see text]), as well as the critical exponents [Formula: see text], [Formula: see text], and [Formula: see text] for several values of the rewiring probability [Formula: see text]. We find that this disordered system does not belong to the same universality class as the regular two-dimensional ferromagnetic model. The majority-vote model on directed small-world lattices presents in fact a second-order phase transition with new critical exponents which do not depend on [Formula: see text] ([Formula: see text]), but agree with the exponents of the equilibrium Ising model on directed small-world Voronoi–Delaunay random lattices.

Sign in / Sign up

Export Citation Format

Share Document