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.

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 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 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 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.

Equilibrium and nonequilibrium models on solomon networks with two square lattices

2017 ◽  
Vol 28 (08) ◽  
pp. 1750099
Author(s):  
F. W. S. Lima
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Critical Exponent ◽  
Critical Points ◽  
Majority Vote ◽  
Universality Class ◽  
2D Systems ◽  
Two Dimensional ◽  
Critical Properties ◽  
Regular Lattices

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios [Formula: see text], [Formula: see text], and [Formula: see text]. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

Equilibrium and nonequilibrium models on Solomon networks

2016 ◽  
Vol 27 (11) ◽  
pp. 1650134 ◽  
Author(s):  
F. W. S. Lima
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Critical Exponents ◽  
Majority Vote ◽  
Universality Class ◽  
Nonequilibrium Systems ◽  
Two Dimensional ◽  
Critical Properties ◽  
The Monte Carlo Method ◽  
Regular Lattices

We investigate the critical properties of the equilibrium and nonequilibrium systems on Solomon networks. The equilibrium and nonequilibrium systems studied here are the Ising and Majority-vote models, respectively. These systems are simulated by applying the Monte Carlo method. We calculate the critical points, as well as the critical exponents ratio [Formula: see text], [Formula: see text] and [Formula: see text]. We find that both systems present identical exponents on Solomon networks and are of different universality class as the regular two-dimensional ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

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.

Surface and Size Effects in TGS, NaNO2, and DKDP Nanocrystals

2000 ◽  
Vol 655 ◽  
Author(s):  
Juan D. Romero ◽  
Luis F. Fonseca ◽  
Rafael Ramos ◽  
Manuel I. Marqués ◽  
Julio A. Gonzalo
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Size Effects ◽  
Paraelectric Phase ◽  
Paraelectric Phase Transition ◽  
Model Hamiltonian ◽  
Phase Transition Temperatures ◽  
Polarization Temperature

AbstractMonte Carlo simulations of some typical order-disorder ferroelectrics such as TGS, NaNO2 and DKDP nanocrystals were studied using a Transverse Ising Model Hamiltonian with four-spins interactions. The microscopic parameters corresponding to this Hamiltonian were adjusted to fit the experimental polarization-temperature curves for each one of the materials in the bulk phase. Then the dependences of the ferroelectric-paraelectric phase transition temperatures, Tc, on the sizes of those crystals were studied with Monte Carlo simulations of the order-disorder system. We report a weak dependence of Tc on the size of the crystal (d) for these materials above d∼6nm. The addition of surface effects showed that the expected lowtemperature shift of Tc due to size effects, can be reverted.

scholarly journals MONTE CARLO SIMULATIONS OF A DISORDERED BINARY ISING MODEL

2012 ◽  
Vol 23 (08) ◽  
pp. 1240015 ◽  
Author(s):  
D. S. CAMBUÍ ◽  
A. S. DE ARRUDA ◽  
M. GODOY
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Critical Exponents ◽  
Nearest Neighbor ◽  
Spin Exchange ◽  
Exchange Interactions ◽  
Square Lattice ◽  
Critical Temperatures

A disordered binary Ising model, with only nearest-neighbor spin exchange interactions J > 0 on the square lattice, is studied through Monte Carlo simulations. The system consists of two different particles with spin-1/2 and spin-1, randomly distributed on the lattice. We found the critical temperatures for several values of the concentration x of spin-1/2 particles, and also the corresponding critical exponents.

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