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 MAJORITY-VOTE MODEL ON OPINION-DEPENDENT NETWORK

2013 ◽  
Vol 24 (09) ◽  
pp. 1350066 ◽  
Author(s):  
F. W. S. LIMA
Keyword(s):  
Monte Carlo ◽  
Majority Vote ◽  
Finite Size ◽  
Universality Class ◽  
Scaling Relations ◽  
Finite Size Scaling ◽  
Vote Model ◽  
Noise Parameter ◽  
Error Bars ◽  
Binder Cumulant

We study a nonequilibrium model with up–down symmetry and a noise parameter q known as majority-vote model (MVM) of Oliveira 1992 on opinion-dependent network or Stauffer–Hohnisch–Pittnauer (SHP) networks. 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 = 0.230(3), γ∕ν = 0.535(2) and 1∕ν = 0.475(8). The calculated values of the critical noise parameter and Binder cumulant are qc = 0.166(3) and U* = 0.288(3). Within the error bars, the exponents obey the relation 2β∕ν + γ∕ν = 1 and the results presented here demonstrate that the MVM belongs to a different universality class than the equilibrium Ising model on SHP networks, but to the same class as majority-vote models on some other networks.

Nonequilibrium model on Archimedean lattices

Open Physics ◽  
2014 ◽  
Vol 12 (3) ◽  
Author(s):  
F. Lima
Keyword(s):  
Majority Vote ◽  
Finite Size ◽  
Stat Phys ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Critical Temperatures ◽  
Vote Model ◽  
Monte Carlo Studies ◽  
Regular Lattices ◽  
Binder Cumulant

AbstractOn (4, 6, 12) and (4, 82) Archimedean lattices, the critical properties of the majority-vote model are considered and studied using the Glauber transition rate proposed by Kwak et al. [Kwak et al., Phys. Rev. E, 75, 061110 (2007)] rather than the traditional majority-vote with noise [Oliveira, J. Stat. Phys. 66, 273 (1992)]. We obtain T c and the critical exponents for this Glauber rate from extensive Monte Carlo studies and finite size scaling. The calculated values of the critical temperatures and Binder cumulant are T c = 0.651(3) and U 4* = 0.612(5), and T c = 0.667(2) and U 4* = 0.613(5), for (4, 6, 12) and (4, 82) lattices respectively, while the exponent (ratios) β/ν, γ/ν and 1/ν are respectively: 0.105(8), 1.48(11) and 1.16(5) for (4, 6, 12); and 0.113(2), 1.60(4) and 0.84(6) for (4, 82) lattices. The usual Ising model and the majority-vote model on previously studied regular lattices or complex networks differ from our new results.

scholarly journals PERCOLATION-LIKE PHASE TRANSITION IN A NONEQUILIBRIUM STEADY STATE

2001 ◽  
Vol 12 (02) ◽  
pp. 247-256
Author(s):  
INDRANI BOSE ◽  
INDRANATH CHAUDHURI
Keyword(s):  
Steady State ◽  
Finite Size ◽  
Reaction Diffusion ◽  
Universality Class ◽  
Critical Value ◽  
Square Lattice ◽  
Finite Size Scaling ◽  
Average Cluster Size ◽  
A Site ◽  
Average Cluster

We study the Gierer–Meinhardt model of reaction-diffusion on a site-disordered square lattice. Let p be the site occupation probability of the square lattice. For p greater than a critical value pc, the steady state consists of stripe-like patterns with long-range connectivity. For p < pc, the connectivity is lost. The value of pc is found to be much greater than that of the site percolation threshold for the square lattice. In the vicinity of pc, the cluster-related quantities exhibit power-law scaling behavior. The method of finite-size scaling is used to determine the values of the fractal dimension df, the ratio, γ/ν, of the average cluster size exponent γ and the correlation length exponent ν. The values appear to indicate that the disordered GM model belongs to the universality class of ordinary percolation.

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.

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

THE SIMULATION OF 2D SPIN-1 ISING MODEL WITH POSITIVE BIQUADRATIC INTERACTION ON A CELLULAR AUTOMATON

2003 ◽  
Vol 14 (10) ◽  
pp. 1305-1320 ◽  
Author(s):  
BÜLENT KUTLU
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Cellular Automaton ◽  
Intermediate Phase ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Antiferromagnetic Spin

The two-dimensional antiferromagnetic spin-1 Ising model with positive biquadratic interaction is simulated on a cellular automaton which based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transition of the model are presented for a comparison with those obtained from other calculations. We confirm the existence of the intermediate phase observed in previous works for some values of J/K and D/K. The values of the static critical exponents (β, γ and ν) are estimated within the framework of the finite-size scaling theory for D/K<2J/K. Although the results are compatible with the universal Ising critical behavior in the region of D/K<2J/K-4, the model does not exhibit any universal behavior in the interval 2J/K-4<D/K<2J/K.

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
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