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.

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 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 Multi-Agent-Based Model on Various Topologies

2017 ◽  
Vol 01 (02) ◽  
pp. 1730001
Author(s):  
F. W. S. Lima
Keyword(s):  
Monte Carlo ◽  
Tax Evasion ◽  
Majority Vote ◽  
Small World ◽  
Stat Phys ◽  
Small World Networks ◽  
Vote Model ◽  
Agent Based ◽  
Multi Agent ◽  
Economics Model

In this work, we use Monte-Carlo simulations to study the control of the fluctuations for tax evasion in the economics model proposed by [G. Zaklan, F. Westerhoff and D. Stauffer, J. Econ. Interact. Coordination. 4 (2009) 1; G. Zaklam, F.W.S. Lima and F. Westerhofd, Physica A 387 (2008) 5857.] via a nonequilibrium model with two states ([Formula: see text]) and a noise [Formula: see text] proposed for [M. J. Oliveira, J. Stat. Phys. 66 (1992) 273] and known as Majority-Vote model (MVM) and Sánchez–López-Rodríguez model on communities of agents or persons on some topologies as directed and undirected Barabási–Albert networks and Erdös–Rényi random graphs, Apollonian networks, directed small-world networks and Stauffer–Hohnisch–Pittnauer networks. The MVM is applied around the noise critical [Formula: see text] to evolve the Zaklan model.

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.

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.

scholarly journals Three-state majority-vote model on small-world networks

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Bernardo J. Zubillaga ◽  
André L. M. Vilela ◽  
Minggang Wang ◽  
Ruijin Du ◽  
Gaogao Dong ◽  
...  
Keyword(s):  
Social Interactions ◽  
Social Order ◽  
Majority Vote ◽  
Small World ◽  
Opinion Dynamics ◽  
Clustering Coefficient ◽  
Square Lattice ◽  
Two Dimensional ◽  
Small World Networks ◽  
Vote Model

AbstractIn this work, we study the opinion dynamics of the three-state majority-vote model on small-world networks of social interactions. In the majority-vote dynamics, an individual adopts the opinion of the majority of its neighbors with probability 1-q, and a different opinion with chance q, where q stands for the noise parameter. The noise q acts as a social temperature, inducing dissent among individual opinions. With probability p, we rewire the connections of the two-dimensional square lattice network, allowing long-range interactions in the society, thus yielding the small-world property present in many different real-world systems. We investigate the degree distribution, average clustering coefficient and average shortest path length to characterize the topology of the rewired networks of social interactions. By employing Monte Carlo simulations, we investigate the second-order phase transition of the three-state majority-vote dynamics, and obtain the critical noise $$q_c$$ q c , as well as the standard critical exponents $$\beta /\nu$$ β / ν , $$\gamma /\nu$$ γ / ν , and $$1/\nu$$ 1 / ν for several values of the rewiring probability p. We conclude that the rewiring of the lattice enhances the social order in the system and drives the model to different universality classes from that of the three-state majority-vote model in two-dimensional square lattices.

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