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

Neto

et al. 2013

Int. J. Mod. Phys. B

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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 ≤ α < 0.25, belongs to the universality class of the three-dimensional pure Ising Model.

Section: Resultsmentioning

confidence: 99%

QUALITATIVE ASPECTS OF THE PHASE DIAGRAM OF J₁–J₂ MODEL ON THE CUBIC LATTICE

Salmon

Neto

et al. 2013

Int. J. Mod. Phys. B

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“…Models of opinion formation are useful to understand the requirements for the upraise of consensus and polarization, when a given issue is under debate [1][2][3][4]. Although interactions between agents are different from those that govern physical systems, similar collective states and transitions between them can emerge [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Symmetry breaking by heating in a continuous opinion model

Anteneodo

2017

Phys. Rev. E

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We study the critical behavior of a continuous opinion model, driven by kinetic exchanges in a fully connected population. Opinions range in the real interval [-1,1], representing the different shades of opinions against and for an issue under debate. Individuals' opinions evolve through pairwise interactions, with couplings that are typically positive, but a fraction p of negative ones is allowed. Moreover, a social temperature parameter T controls the tendency of the individual responses toward neutrality. Depending on p and T, different collective states emerge: symmetry broken (one side wins), symmetric (tie of opposite sides), and absorbing neutral (indecision wins). We find the critical points and exponents that characterize the phase transitions between them. The symmetry breaking transition belongs to the usual Ising mean-field universality class, but the absorbing-phase transitions, with β=0.5, are out of the paradigmatic directed percolation class. Moreover, ordered phases can emerge by increasing social temperature.

“…The universality of the exponents is expected due to the mean-field character of the model. As extensions of this work, it can be considered the inclusion of local or global mass media effects [5,41], as well as the inclusion of a neighborhood (lattice, network).…”

Section: Final Remarksmentioning

confidence: 99%

Noise-induced absorbing phase transition in a model of opinion formation

Vieira

2016

Physics Letters A

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In this work we study a 3-state (+1, −1, 0) opinion model in the presence of noise and disorder. We consider pairwise competitive interactions, with a fraction p of those interactions being negative (disorder). Moreover, there is a noise q that represents the probability of an individual spontaneously change his opinion to the neutral state. Our aim is to study how the increase/decrease of the fraction of neutral agents affects the critical behavior of the system and the evolution of opinions. We derive analytical expressions for the order parameter of the model, as well as for the stationary fraction of each opinion, and we show that there are distinct phase transitions. One is the usual ferro-paramagnetic transition, that is in the Ising universality class. In addition, there are para-absorbing and ferro-absorbing transitions, presenting the directed percolation universality class. Our results are complemented by numerical simulations.