Isotropic majority-vote model on a square lattice

1992 ◽  
Vol 66 (1-2) ◽  
pp. 273-281 ◽  
Author(s):  
M. J. de Oliveira
Keyword(s):  
Majority Vote ◽  
Square Lattice ◽  
Vote Model

scholarly journals MAJORITY-VOTE MODEL WITH HETEROGENEOUS AGENTS ON SQUARE LATTICE

2013 ◽  
Vol 24 (11) ◽  
pp. 1350083 ◽  
Author(s):  
F. W. S. LIMA
Keyword(s):  
Heterogeneous Agents ◽  
Majority Vote ◽  
Finite Size ◽  
Universality Class ◽  
Square Lattice ◽  
Stat Phys ◽  
Finite Size Scaling ◽  
Vote Model ◽  
Noise Parameter ◽  
Binder Cumulant

We study a nonequilibrium model with up-down symmetry and a noise parameter q known as majority-vote model (MVM) of [M. J. Oliveira, J. Stat. Phys.66, 273 (1992)] with heterogeneous agents on square lattice (SL). By Monte Carlo (MC) simulations and finite-size scaling relations, the critical exponents β∕ν, γ∕ν and 1∕ν and points qc and U* are obtained. After extensive simulations, we obtain β∕ν = 0.35(1), γ∕ν = 1.23(8) and 1∕ν = 1.05(5). The calculated values of the critical noise parameter and Binder cumulant are qc = 0.1589(4) and U* = 0.604(7). Within the error bars, the exponents obey the relation 2β∕ν + γ∕ν = 2 and the results presented here demonstrate that the MVM heterogeneous agents belongs to a different universality class than the nonequilibrium MVM with homogeneous agents on SL.

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.

scholarly journals Three-State Majority-Vote Model on Small-World Networks

2021 ◽  
Author(s):  
Bernardo J. Zubillaga ◽  
André L. M. Vilela ◽  
Minggang Wang ◽  
Ruijin Du ◽  
Gaogao Dong ◽  
...  
Keyword(s):  
Social Order ◽  
Majority Vote ◽  
Small World ◽  
Opinion Dynamics ◽  
Square Lattice ◽  
Two Dimensional ◽  
Small World Networks ◽  
Vote Model ◽  
Lattice Network ◽  
Small World Property

Abstract In 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 the dissensus 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 employ Monte Carlo simulations to investigate the second-order phase transition of the system, and obtain the critical noise qc, as well as the standard critical exponents β/ν, γ/ν, and 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.

scholarly journals Three-state majority-vote model on square lattice

2012 ◽  
Vol 391 (4) ◽  
pp. 1753-1758 ◽  
Author(s):  
F.W.S. Lima
Keyword(s):  
Majority Vote ◽  
Square Lattice ◽  
Vote Model

scholarly journals Statistics of opinion domains of the majority-vote model on a square lattice

2010 ◽  
Vol 82 (4) ◽  
Author(s):  
Lucas R. Peres ◽  
José F. Fontanari
Keyword(s):  
Majority Vote ◽  
Square Lattice ◽  
Vote Model

Tax evasion dynamics and nonequilibrium Zaklan model with heterogeneous agents on square lattice

2015 ◽  
Vol 26 (03) ◽  
pp. 1550035
Author(s):  
F. W. S. Lima
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Time Evolution ◽  
Tax Evasion ◽  
Heterogeneous Agents ◽  
Majority Vote ◽  
Square Lattice ◽  
Vote Model ◽  
Agent Based ◽  
Nonequilibrium Model

In this paper, we use the version of the nonequilibrium Zaklan model via agent-based Monte-Carlo simulations to study the problem of the fluctuations of the tax evasion on a heterogeneous agents community of honest and tax evaders citizens. The time evolution of this system is performed by a nonequilibrium model known as majority-vote model, but with a different probability for each agent to disobey the majority vote of its neighbors.

scholarly journals Large deviation induced phase switch in an inertial majority-vote model

2017 ◽  
Vol 27 (8) ◽  
pp. 081102 ◽  
Author(s):  
Hanshuang Chen ◽  
Chuansheng Shen ◽  
Haifeng Zhang ◽  
Jürgen Kurths
Keyword(s):  
Large Deviation ◽  
Majority Vote ◽  
Vote Model

scholarly journals Fundamental ingredients for discontinuous phase transitions in the inertial majority vote model

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Jesus M. Encinas ◽  
Pedro E. Harunari ◽  
M. M. de Oliveira ◽  
Carlos E. Fiore
Keyword(s):  
Phase Transitions ◽  
Majority Vote ◽  
Vote Model ◽  
Discontinuous Phase ◽  
Discontinuous Phase Transitions

scholarly journals Effect of Strong Opinions on the Dynamics of the Majority-Vote Model

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
André L. M. Vilela ◽  
H. Eugene Stanley
Keyword(s):  
Majority Vote ◽  
Vote Model
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