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F. W. S. Lima

Publications and source records attributed to F. W. S. Lima.

At least 37 records · Page 2Linked to original sources
arXiv2013

Majority-vote model with heterogeneous agents on square lattice

We study a nonequilibrium model with up-down symmetry and a noise parameter $q$ known as majority-vote model of M.J. Oliveira 1992 with heterogeneous agents on square lattice. By Monte Carlo simulations and finite-size scaling relations the critical exponents $β/ν$, $γ/ν$, and $1/ν$ and points $q_{c}$ 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 $q_{c}=0.1589(4)$ 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 majority-vote model heterogeneous agents belongs to a different universality class than the nonequilibrium majority-vote models with homogeneous agents on square lattice.

physics.soc-ph↗
arXiv2013

Ising model on directed small-world Voronoi Delaunay random lattices

We investigate the critical properties of the Ising model in two dimensions on {\it directed} small-world lattice with quenched connectivity disorder. The disordered system is simulated by applying the Monte Carlo update heat bath algorithm. We calculate the critical temperature, as well as the critical exponents $γ/ν$, $β/ν$, and $1/ν$ for several values of the rewiring probability $p$. We find that this disorder system does not belong to the same universality class as the regular two-dimensional ferromagnetic model. The Ising model on {\it directed} small-world lattices presents in fact a second-order phase transition with new critical exponents which do not dependent of $p$, but are identical to the exponents of the Ising model and the spin-1 Blume-Capel model on {\it directed} small-world network.

cond-mat.dis-nn↗
arXiv2013

Majority-vote model on Opinion-Dependent Networks

We study a nonequilibrium model with up-down symmetry and a noise parameter $q$ known as majority-vote model of M.J. Oliveira $1992$ on opinion-dependent network or Stauffer-Hohnisch-Pittnauer networks. By Monte Carlo simulations and finite-size scaling relations the critical exponents $β/ν$, $γ/ν$, and $1/ν$ and points $q_{c}$ 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 $q_{c}=0.166(3)$ 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 majority-vote model belongs to a different universality class than the equilibrium Ising model on Stauffer-Hohnisch-Pittnauer networks, but to the same class as majority-vote models on some other networks.

physics.soc-ph↗
arXiv2013

Majority-vote model on (3,12^2), (4,6,12) and (4,8^2) Archimedean lattices

On ($3,12^2$), ($4,6,12$) and ($4,8^2$) Archimedean lattices, the critical properties of majority-vote model are considered and studied using the Glauber transition rate proposed by Kwak {\it et all.} [Phys. Rev. E, {\bf 75}, 061110 (2007)] rather than the traditional majority-vote with noise [José Mário de Oliveira, J. Stat. Phys. {\bf 66}, 273 (1992)]. The critical temperature and the critical exponents for this transition rate are obtained from extensive Monte Carlo simulations and with a finite size scaling analysis. The calculated values of the critical temperatures Binder cumulant are $T_c=0.363(2)$ and $U_4^*=0.577(4)$; $T_c=0.651(3)$ and $U_4^*=0.612(5)$; and $T_c=0.667(2)$ and $U_4^*=0.613(5)$ for ($3,12^2$), ($4,6,12$) and ($4,8^2$) lattices, respectively. The critical exponents $β/ν$, $γ/ν$ and $1/ν$ for this model are $0.237(6)$, $0.73(10)$, and $ 0.83(5)$; $0.105(8)$, $1.28(11)$, and $1.16(5)$; $0.113(2)$, $1.60(4)$, and $0.84(6)$ for ($3,12^2$), ($4,6,12$) and ($4,8^2$) lattices, respectively. These results differ from the usual Ising model results and the majority-vote model on so-far studied regular lattices or complex networks.

physics.soc-ph↗
arXiv2012

Potts model with q=3 and 4 states on directed Small-World network

Monte Carlo simulations are performed to study the two-dimensional Potts models with q=3 and 4 states on directed Small-World network. The disordered system is simulated applying the Heat bath Monte Carlo update algorithm. A first-order and second-order phase transition is found for q=3 depending on the rewiring probability $p$, but for q=4 the system presents only a first-order phase transition for any value $p$ . This critical behavior is different from the Potts model on a square lattice, where the second-order phase transition is present for $q\le4$ and a first-order phase transition is present for q>4.

cond-mat.stat-mech↗
arXiv2012

Nonequilibrium Zaklan model on Apollonian Networks

The Zaklan model had been proposed and studied recently using the equilibrium Ising model on Square Lattices (SL) by Zaklan et al (2008), near the critica temperature of the Ising model presenting a well-defined phase transition; but on normal and modified Apollonian networks (ANs), Andrade et al. (2005, 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 $q_{c}$ to the Zaklan model. Here we show that the Zaklan model is robust because this can be studied besides using equilibrium dynamics of Ising model also through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.

physics.soc-ph↗
arXiv2012

Non-nequilibrium model on Apollonian networks

We investigate the Majority-Vote Model with two states ($-1,+1$) and a noise $q$ on Apollonian networks. The main result found here is the presence of the phase transition as a function of the noise parameter $q$. We also studies de effect of redirecting a fraction $p$ of the links of the network. By means of Monte Carlo simulations, we obtained the exponent ratio $γ/ν$, $β/ν$, and $1/ν$ for several values of rewiring probability $p$. The critical noise was determined $q_{c}$ and $U^{*}$ also was calculated. The effective dimensionality of the system was observed to be independent on $p$, and the value $D_{eff} \approx1.0$ is observed for these networks. Previous results on the Ising model in Apollonian Networks have reported no presence of a phase transition. Therefore, the results present here demonstrate that the Majority-Vote Model belongs to a different universality class as the equilibrium Ising Model on Apollonian Network.

physics.soc-ph↗
arXiv2012

Tax evasion dynamics and Zaklan model on Opinion-dependent Network

Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on Stauffer-Hohnisch-Pittnauer (SHP) networks. To control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhood of the critical noise $q_{c}$ to evolve the Zaklan model. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust because this can be studied besides using equilibrium dynamics of Ising model also through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.

physics.soc-ph↗
arXiv2011

Three-state majority-vote model on square lattice

Here, the model of non-equilibrium model with two states ($-1,+1$) and a noise $q$ on simple square lattices proposed for M.J. Oliveira (1992) following the conjecture of up-down symmetry of Grinstein and colleagues (1985) is studied and generalized. This model is well-known, today, as Majority-Vote Model. They showed, through Monte Carlo simulations, that their obtained results fall into the universality class of the equilibrium Ising model on a square lattice. In this work, we generalize the Majority-Vote Model for a version with three states, now including the zero state, ($-1,0,+1$) in two dimensions. Using Monte Carlo simulations, we showed that our model falls into the universality class of the spin-1 ($-1,0,+1$) and spin-1/2 Ising model and also agree with Majority-Vote Model proposed for M.J. Oliveira (1992) . The exponents ratio obtained for our model was $γ/ν=1.77(3)$, $β/ν=0.121(5)$, and $1/ν=1.03(5)$. The critical noise obtained and the fourth-order cumulant were $q_{c}=0.106(5)$ and $U^{*}=0.62(3)$.

physics.soc-ph↗
arXiv2011

Ising model with spins S=1/2 and 1 on directed and undirected Erdös-Rényi random graphs

Using Monte Carlo simulations we study the Ising model with spin S=1/2 and 1 on {\it directed} and {\it undirected} Erdös-Rényi (ER) random graphs, with $z$ neighbors for each spin. In the case with spin S=1/2, the {\it undirected} and {\it directed} ER graphs present a spontaneous magnetization in the universality class of mean field theory, where in both {\it directed} and {\it undirected} ER graphs the model presents a spontaneous magnetization at $p = z/N$ ($z=2, 3, ...,N$), but no spontaneous magnetization at $p = 1/N$ which is the percolation threshold. For both {\it directed} and {\it undirected} ER graphs with spin S=1 we find a first-order phase transition for z=4 and 9 neighbors.

cond-mat.dis-nn↗
arXiv2010

Majority-vote model on triangular, honeycomb and Kagome lattices

On Archimedean lattices, the Ising model exhibits spontaneous ordering. Three 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 q_c=0.089(5), q_c=0.078(3), and q_c=0.114(2) for honeycomb, Kagome and triangular lattices, respectively. The critical exponents beta/nu, gamma/nu and 1/nu for this model are 0.15(5), 1.64(5), and 0.87(5); 0.14(3), 1.64(3), and 0.86(6); 0.12(4), 1.59(5), and 1.08(6) for honeycomb, Kagome and triangular lattices, respectively. 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}= 1.96(5) (honeycomb), D_{eff} =1.92(4) (Kagome), and D_{eff}= 1.83(5) (triangular) for these networks are just compatible to the embedding dimension two.

cond-mat.stat-mech↗
arXiv2010

Critical behaviour of the Ising S=1/2 and S=1 model on (3,4,6,4) and (3,3,3,3,6) Archimedean lattices

We investigate the critical properties of the Ising S=1/2 and S=1 model on (3,4,6,4) and (3,3,3,3,6) Archimedean lattices. The system is studied through the extensive Monte Carlo simulations. We calculate the critical temperature as well as the critical point exponents gamma/nu, beta/nu and nu basing on finite size scaling analysis. The calculated values of the critical temperature for S=1 are k_BT_C/J=1.590(3) and k_BT_C/J=2.100(4) for (3,4,6,4) and (3,3,3,3,6) Archimedean lattices, respectively. The critical exponents beta/nu, gamma/nu and 1/nu for S=1 are beta/nu=0.180(20), gamma/nu=1.46(8) and 1/nu=0.83(5) for (3,4,6,4) and 0.103(8), 1.44(8) and 0.94(5) for (3,3,3,3,6) Archimedean lattices. Obtained results differ from the Ising S=1/2 model on (3,4,6,4), (3,3,3,3,6) and square lattice. The evaluated effective dimensionality of the system for S=1 are D_{eff}=1.82(4) for (3,4,6,4) and D_{eff}=1.64(5) for (3,3,3,3,6).

cond-mat.stat-mech↗
arXiv2010

Blume-Capel model on directed and undirected Small-World Voronoi-Delaunay random lattices

The critical properties of the spin-1 two-dimensional Blume-Capel model on directed and undi- rected random lattices with quenched connectivity disorder is studied through Monte Carlo simulations. The critical temperature, as well as the critical point exponents are obtained. For the undi- rected case this random system belongs to the same universality class as the regular two-dimensional model. However, for the directed random lattice one has a second-order phase transition for q < qc and a first-order phase transition for q > qc, where qc is the critical rewiring probability. The critical exponents for q < qc was calculated and they do not belong to the same universality class as the regular two-dimensional ferromagnetic model.

cond-mat.stat-mech↗
arXiv2010

Potts model with $q=4,6,$ and 8 states on Voronoi-Delaunay random lattice

Through Monte Carlo simulations we study two-dimensional Potts models with $q=4, 6$ and 8 states on Voronoi-Delaunay random lattice. In this study, we assume that the coupling factor $J$ varies with the distance $r$ between the first neighbors as $J(r)\propto e^{-a r}$, with $a \geq 0$ . The disordered system is simulated applying the singler-cluster Monte Carlo update algorithm and reweigting technique. In this model both second-order and first-order phase transition are present depending of $q$ values and $a$ parameter. The critical exponents ratio $β/ν$, $γ/ν$, and $1/ν$ were calculated for case where the second-order phase transition are present. In the Potts model with $q=8$ we also studied the distribution of clusters sizes.

cond-mat.dis-nn↗
arXiv2009

Analysing and controlling the tax evasion dynamics via majority-vote model

Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on simple square lattices, Voronoi-Delaunay random lattices, Barabasi-Albert networks, and Erdös-Rényi random graphs. In the order to analyse and to control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhod of the noise critical $q_{c}$. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust and can be reproduced also through the nonequilibrium MVM on various topologies.

physics.soc-ph↗
arXiv2009

Evolution of ethnocentrism on undirected and directed Barabási-Albert networks

Using Monte Carlo simulations, we study the evolution of contigent cooperation and ethnocentrism in the one-move game. Interactions and reproduction among computational agents are simulated on {\it undirected} and {\it directed} Barabási-Albert (BA) networks. We first replicate the Hammond-Axelrod model of in-group favoritism on a square lattice and then generalize this model on {\it undirected} and {\it directed} BA networks for both asexual and sexual reproduction cases. Our simulations demonstrate that irrespective of the mode of reproduction, ethnocentric strategy becomes common even though cooperation is individually costly and mechanisms such as reciprocity or conformity are absent. Moreover, our results indicate that the spread of favoritism toward similar others highly depends on the network topology and the associated heterogeneity of the studied population.

physics.soc-ph↗
arXiv2008

Persistence in the zero-temperature dynamics of the $Q$-states Potts model on undirected-directed Barabási-Albert networks and Erdös-Rényi random graphs

The zero-temperature Glauber dynamics is used to investigate the persistence probability $P(t)$ in the Potts model with $Q=3,4,5,7,9,12,24,64, 128$, $256, 512, 1024,4096,16384 $,..., $2^{30}$ states on {\it directed} and {\it undirected} Barabási-Albert networks and Erdös-Rényi random graphs. In this model it is found that $P(t)$ decays exponentially to zero in short times for {\it directed} and {\it undirected} Erdös-Rényi random graphs. For {\it directed} and {\it undirected} Barabási-Albert networks, in contrast it decays exponentially to a constant value for long times, i.e, $P(\infty)$ is different from zero for all $Q$ values (here studied) from $Q=3,4,5,..., 2^{30}$; this shows "blocking" for all these $Q$ values. Except that for $Q=2^{30}$ in the {\it undirected} case $P(t)$ tends exponentially to zero; this could be just a finite-size effect since in the other "blocking" cases you may have only a few unchanged spins.

cond-mat.stat-mech↗