arXiv subjects

Nuno Crokidakis

Publications and source records attributed to Nuno Crokidakis.

70 records · Page 4Linked to original sources

arXiv2013

Qualitative aspects of the phase diagram of J1-J2 model on the cubic lattice

The qualitative aspects of the phase diagram of the Ising model on the cubic lattice, with ferromagnetic nearest-neighbor interactions ($J_{1}$) and antiferromagnetic next-nearest-neighbor couplings ($J_{2}$) are analyzed in the plane temperature versus $α$, where $α=J_{2}/|J_{1}|$ is the frustration parameter. We used the original Wang-Landau sampling and the standard Metropolis algorithm to confront past results of this model obtained by the effective-field theory (EFT) for the cubic lattice. Our numerical results suggest that the predictions of the EFT are in general qualitatively correct, but the low-temperature reentrant behavior, observed in the frontier separating the ferromagnetic and the colinear order, is an artifact of the EFT approach and should disappear when we consider Monte Carlo simulations of the model. In addition, our results indicate that the continuous phase transition between the Ferromagnetic and the Paramagnetic phases, that occurs for $0.0 \leq α< 0.25$, belongs to the universality class of the three-dimensional pure Ising Model.

cond-mat.stat-mech↗

arXiv2013

Role of noise and agents' convictions on opinion spreading in a three-state voter-like model

In this work we study the opinion formation in a voter-like model defined on a square lattice of linear size $L$. The agents may be in three different states, representing any public debate with three choices (yes, no, undecided). We consider heterogeneous agents that have different convictions about their opinions. These convictions limit the capacity of persuasion of the individuals during the interactions. Moreover, there is a noise $p$ that represents the probability of an individual spontaneously change his opinion to the undecided state. Our simulations suggest that the system reaches stationary states for all values of $p$, with consensus states occurring only for the noiseless case $p=0$. In this case, the relaxation times are distributed according to a log-normal function, with the average value $τ$ growing with the lattice size as $τ\sim L^α$, where $α\approx$ 0.9. We found a threshold value $p^{*}\approx$ 0.9 above which the stationary fraction of undecided agents is greater than the fraction of decided ones. We also study the consequences of the presence of external effects in the system, which models the influence of mass media on opinion formation.

physics.soc-ph↗

arXiv2012

Information spreading with aging in heterogeneous populations

We study the critical properties of a model of information spreading based on the SIS epidemic model. Spreading rates decay with time, as ruled by two parameters, $ε$ and $l$, that can be either constant or randomly distributed in the population. The spreading dynamics is developed on top of Erdös-Renyi networks. We present the mean-field analytical solution of the model in its simplest formulation, and Monte Carlo simulations are performed for the more heterogeneous cases. The outcomes show that the system undergoes a nonequilibrium phase transition whose critical point depends on the parameters $ε$ and $l$. In addition, we conclude that the more heterogeneous the population, the more favored the information spreading over the network.

physics.soc-ph↗

arXiv2012

Role of conviction in nonequilibrium models of opinion formation

We analyze the critical behavior of a class of discrete opinion models in the presence of disorder. Within this class, each agent opinion takes a discrete value ($\pm 1$ or 0) and its time evolution is ruled by two terms, one representing agent-agent interactions and the other the degree of conviction or persuasion (a self-interaction). The mean-field limit, where each agent can interact evenly with any other, is considered. Disorder is introduced in the strength of both interactions, with either quenched or annealed random variables. With probability $p$ (1-$p$), a pairwise interaction reflects a negative (positive) coupling, while the degree of conviction also follows a binary probability distribution (two different discrete probability distributions are considered). Numerical simulations show that a non-equilibrium continuous phase transition, from a disordered state to a state with a prevailing opinion, occurs at a critical point $p_{c}$ that depends on the distribution of the convictions, the transition being spoiled in some cases. We also show how the critical line, for each model, is affected by the update scheme (either parallel or sequential) as well as by the kind of disorder (either quenched or annealed).

physics.soc-ph↗

arXiv2012

Impact of site dilution and agent diffusion on the critical behavior of the majority-vote model

In this work we study a modified version of the majority-vote model with noise. In particular, we consider a random diluted square lattice for which a site is empty with a probability $r$. In order to analyze the critical behavior of the model, we perform Monte Carlo simulations on lattices with linear sizes up to L=140. By means of a finite-size scaling analysis we estimate the critical noises $q_{c}$ and the critical ratios $β/ν$, $γ/ν$ and $1/ν$ for some values of the probability $r$.

physics.soc-ph↗

arXiv2012

Probing into the effectiveness of self-isolation policies in epidemic control

In this work, we inspect the reliability of controlling and quelling an epidemic disease mimicked by a Susceptible-Infected-Susceptible (SIS) model defined on a complex network by means of current and implementable quarantine and isolation policies. Specifically, we consider that each individual in the network is originally linked to two types of individuals: members of the same household and acquaintances. The topology of this network evolves taking into account a probability $q$ that aims at representing the quarantine or isolation process in which the connection with acquaintances is disrupted according to standard policies of control of epidemics. Within current policies of self-isolation and standard infection rates, our results show that the propagation is either only controllable for hypothetical rates of compliance or uncontrollable at all.

q-bio.PE↗

arXiv2012

Critical behavior of the SIS epidemic model with time-dependent infection rate

In this work we study a modified Susceptible-Infected-Susceptible (SIS) model in which the infection rate $λ$ decays exponentially with the number of reinfections $n$, saturating after $n=l$. We find a critical decaying rate $ε_{c}(l)$ above which a finite fraction of the population becomes permanently infected. From the mean-field solution and computer simulations on hypercubic lattices we find evidences that the upper critical dimension is 6 like in the SIR model, which can be mapped in ordinary percolation.

physics.soc-ph↗

arXiv2011

Competition among reputations in the 2D Sznajd model: Spontaneous emergence of democratic states

We propose a modification in the Sznajd sociophysics model defined on the square lattice. For this purpose, we consider reputation-a mechanism limiting the agents' persuasive power. The reputation is introduced as a time-dependent score, which can be positive or negative. This mechanism avoids dictatorship (full consensus, all spins parallel) for a wide range of model parameters. We consider two different situations: case 1, in which the agents' reputation increases for each persuaded neighbor, and case 2, in which the agents' reputation increases for each persuasion and decreases when a neighbor keeps his opinion. Our results show that the introduction of reputation avoids full consensus even for initial densities of up spins greater than 1/2. The relaxation times follow a log-normal-like distribution in both cases, but they are larger in case 2 due to the competition among reputations. In addition, we show that the usual phase transition occurs and depends on the initial concentration $d$ of individuals with the same opinion, but the critical points $d_{c}$ in the two cases are different.

physics.soc-ph↗

arXiv2011

Effects of mass media on opinion spreading in the Sznajd sociophysics model

In this work we consider the influence of mass media in the dynamics of the two-dimensional Sznajd model. This influence acts as an external field, and it is introduced in the model by means of a probability $p$ of the agents to follow the media opinion. We performed Monte Carlo simulations on square lattices with different sizes, and our numerical results suggest a change on the critical behavior of the model, with the absence of the usual phase transition for $p>\sim 0.18$. Another effect of the probability $p$ is to decrease the average relaxation times $τ$, that are log-normally distributed, as in the standard model. In addition, the $τ$ values depend on the lattice size $L$ in a power-law form, $τ\sim L^α$, where the power-law exponent depends on the probability $p$.

physics.soc-ph↗

arXiv2011

The Sznajd model with limited persuasion: competition between high-reputation and hesitant agents

In this work we study a modified version of the two-dimensional Sznajd sociophysics model. In particular, we consider the effects of agents' reputations in the persuasion rules. In other words, a high-reputation group with a common opinion may convince their neighbors with probability $p$, which induces an increase of the group's reputation. On the other hand, there is always a probability $q=1-p$ of the neighbors to keep their opinions, which induces a decrease of the group's reputation. These rules describe a competition between groups with high reputation and hesitant agents, which makes the full-consensus states (with all spins pointing in one direction) more difficult to be reached. As consequences, the usual phase transition does not occur for $p<p_{c} \sim 0.69$ and the system presents realistic democracy-like situations, where the majority of spins are aligned in a certain direction, for a wide range of parameters.

physics.soc-ph↗

arXiv2010

Fat-tailed and compact random-field Ising models on cubic lattices

Using a single functional form which is able to represent several different classes of statistical distributions, we introduce a preliminary study of the ferromagnetic Ising model on the cubic lattices under the influence of non-Gaussian local external magnetic field. Specifically, depending on the value of the tail parameter, $τ$ ($τ< 3$), we assign a quenched random field that can be platykurtic (sub-Gaussian) or leptokurtic (fat-tailed) form. For $τ< 5/3$, such distributions have finite standard deviation and they are either the Student-$t$ ($1< τ< 5/3$) or the $r$-distribution ($τ< 1$) extended to all plausible real degrees of freedom with the Gaussian being retrieved in the limit $τ\rightarrow 1$. Otherwise, the distribution has got the same asymptotic power-law behaviour as the $α$-stable Lévy distribution with $α= (3 - τ)/(τ- 1)$. The uniform distribution is achieved in the limit $τ\rightarrow \infty$. Our results purport the existence of ferromagnetic order at finite temperatures for all the studied values of $τ$ with some mean-field predictions surviving in the three-dimensional case.

cond-mat.dis-nn↗

arXiv2010

Consequence of reputation in the Sznajd consensus model

In this work we study a modified version of the Sznajd sociophysics model. In particular we introduce reputation, a mechanism that limits the capacity of persuasion of the agents. The reputation is introduced as a score which is time-dependent, and its introduction avoid dictatorship (all spins parallel) for a wide range of parameters. The relaxation time follows a log-normal-like distribution. In addition, we show that the usual phase transition also occurs, as in the standard model, and it depends on the initial concentration of individuals following an opinion, occurring at a initial density of up spins greater than $1/2$. The transition point is determined by means of a finite-size scaling analysis.

physics.soc-ph↗

arXiv2010

Nonequilibrium phase transitions and tricriticality in a three-dimensional lattice system with random-field competing kinetics

We study a nonequilibrium Ising model that stochastically evolves under the simultaneous operation of several spin-flip mechanisms. In other words, the local magnetic fields change sign randomly with time due to competing kinetics. This dynamics models a fast and random diffusion of disorder that takes place in dilute metallic alloys when magnetic ions diffuse. We performe Monte Carlo simulations on cubic lattices up to L=60. The system exhibits ferromagnetic and paramagnetic steady states. Our results predict first-order transitions at low temperatures and large disorder strengths, which correspond to the existence of a nonequilibrium tricritical point at finite temperature. By means of standard finite-size scaling equations, we estimate the critical exponents in the low-field region, for which our simulations uphold continuous phase transitions.

cond-mat.stat-mech↗

arXiv2009

Effect of platy- and leptokurtic distributions in the random-field Ising model: Mean field approach

The influence of the tail features of the local magnetic field probability density function (PDF) on the ferromagnetic Ising model is studied in the limit of infinite range interactions. Specifically, we assign a quenched random field whose value is in accordance with a generic distribution that bears platykurtic and leptokurtic distributions depending on a single parameter $τ< 3$ to each site. For $τ< 5/3$, such distributions, which are basically Student-$t$ and $r$-distribution extended for all plausible real degrees of freedom, present a finite standard deviation, if not the distribution has got the same asymptotic power-law behavior as a $α$-stable Lévy distribution with $α= (3 - τ)/(τ- 1)$. For every value of $τ$, at specific temperature and width of the distribution, the system undergoes a continuous phase transition. Strikingly, we impart the emergence of an inflexion point in the temperature-PDF width phase diagrams for distributions broader than the Cauchy-Lorentz ($τ= 2$) which is accompanied with a divergent free energy per spin (at zero temperature).

cond-mat.stat-mech↗

arXiv2009

Emergence of Clusters in Growing Networks with Aging

We study numerically a model of nonequilibrium networks where nodes and links are added at each time step with aging of nodes and connectivity- and age-dependent attachment of links. By varying the effects of age in the attachment probability we find, with numerical simulations and scaling arguments, that a giant cluster emerges at a first-order critical point and that the problem is in the universality class of one dimensional percolation. This transition is followed by a change in the giant cluster's topology from tree-like to quasi-linear, as inferred from measurements of the average shortest-path length, which scales logarithmically with system size in one phase and linearly in the other.

cond-mat.stat-mech↗

arXiv2008

Multicritical Behavior in a Random-Field Ising Model under a Continuous-Field Probability Distribution

A random-field Ising model that is capable of exhibiting a rich variety of multicritical phenomena, as well as a smearing of such behavior, is investigated. The model consists of an infinite-range-interaction Ising ferromagnet in the presence of a triple-Gaussian random magnetic field, which is defined as a superposition of three Gaussian distributions with the same width $σ$, centered at H=0 and $H=\pm H_{0}$, with probabilities $p$ and $(1-p)/2$, respectively. Such a distribution is very general and recovers as limiting cases, the trimodal, bimodal, and Gaussian probability distributions.

cond-mat.stat-mech↗