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 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.

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 TAX EVASION DYNAMICS AND ZAKLAN MODEL ON OPINION-DEPENDENT NETWORK

2012 ◽  
Vol 23 (06) ◽  
pp. 1250047 ◽  
Author(s):  
F. W. S. LIMA
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Tax Evasion ◽  
Evolutionary Dynamics ◽  
Majority Vote ◽  
Vote Model ◽  
Agent Based ◽  
Non Equilibrium

Within the context of agent-based Monte-Carlo simulations, we study the problem of the fluctuations of tax evasion in a community of honest citizens and tax evaders by using the version of the nonequilibrium Zaklan model proposed by Lima (2010). The studied evolutionary dynamics of tax evasion are driven by a non-equilibrium majority-vote model of M. J. Oliveira, with the objective to attempt to control the fluctuations of the tax evasion in the observed community in which citizens are localized on the nodes of the Stauffer–Hohnisch–Pittnauer networks.

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.

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.

Phase Transition in 2D Anisotropic Ising Model with Next-Nearest Neighbor Interactions in a Magnetic Field

SPIN ◽  
2018 ◽  
Vol 08 (03) ◽  
pp. 1850010
Author(s):  
D. Farsal ◽  
M. Badia ◽  
M. Bennai
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Phase Diagram ◽  
Monte Carlo ◽  
Magnetic Susceptibility ◽  
Critical Temperature ◽  
Ising Model ◽  
Nearest Neighbor ◽  
Two Dimensional ◽  
The Magnetic Field

The critical behavior at the phase transition of the ferromagnetic two-dimensional anisotropic Ising model with next-nearest neighbor (NNN) couplings in the presence of the field is determined using mainly Monte Carlo (MC) method. This method is used to investigate the phase diagram of the model and to verify the existence of a divergence at null temperature which often appears in two-dimensional systems. We analyze also the influence of the report of the NNN interactions [Formula: see text] and the magnetic field [Formula: see text] on the critical temperature of the system, and we show that the critical temperature depends on the magnetic field for positive values of the interaction. Finally, we have investigated other thermodynamical qualities such as the magnetic susceptibility [Formula: see text]. It has been shown that their thermal behavior depends qualitatively and quantitatively on the strength of NNN interactions and the magnetic field.

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 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.

SPECTRUM OF SCREENING MASSES FOR SU(2) GAUGE THEORY: UNIVERSALITY CLASS

2010 ◽  
Vol 19 (08n10) ◽  
pp. 1725-1729
Author(s):  
R. S. COSTA ◽  
S. B. DUARTE ◽  
M. CHIAPPARINI ◽  
T. MENDES
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Gauge Theory ◽  
Critical Temperature ◽  
Variational Method ◽  
Excited States ◽  
Universality Class ◽  
Yang Mills ◽  
Exponential Method ◽  
Deconfinement Phase Transition

In this work we study the spectrum of the lowest screening masses for Yang–Mills theories on the lattice. We used the SU(2) gauge group in (3 + 1) dmensions. We adopted the multiple exponential method and the so-called "variational" method, in order to detect possible excited states. The calculations were done near the critical temperature of the confinement-deconfinement phase transition. We obtained values for the ratios of the screening masses consistent with predictions from universality arguments. A Monte Carlo evolution of the screening masses in the gauge theory confirms the validity of the predictions.

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