Krzysztof Malarz

TRUTH SEEKERS IN OPINION DYNAMICS MODELS

We modify the model of Deffuant et al. to distinguish true opinion among others in the fashion of Hegselmann and Krause (). The basic features of both models modified to account for truth seekers are qualitatively the same.We modify the model of Deffuant et al. to distinguish true opinion among others in the fashion of Hegselmann and Krause<http://jasss.soc.surrey.ac.uk/9/3/10.html>. The basic features of both models modified to account for truth seekers are qualitatively the same.

RESHUFFLING SPINS WITH SHORT RANGE INTERACTIONS: WHEN SOCIOPHYSICS PRODUCES PHYSICAL RESULTS

Galam reshuffling introduced in opinion dynamics models, is investigated under the nearest neighbor Ising model on a square lattice using Monte Carlo simulations. While the corresponding Galam analytical critical temperature TC≈3.09 [J/kB] is recovered almost exactly, it is proved to be different from both values, not reshuffled (TC =2/arcsinh (1)≈2.27 [J/kB]) and mean-field (TC =4 [J/kB]). On this basis, gradual reshuffling is studied as function of 0≤p≤1 where p measures the probability of spin reshuffling after each Monte Carlo step. The variation of TC as function of p is obtained and exhibits a nonlinear behavior. The simplest Solomon network realization is noted to reproduce Galam p =1 result. Similarly to the critical temperature, critical exponents are found to differ from both, the classical Ising case and the mean field values.

Majority-vote model on triangular, honeycomb and Kagomé 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 qc=0.089(5), qc=0.078(3), and qc=0.114(2) for honeycomb, Kagome and triangular lattices, respectively. The critical exponents β/ν, γ/ν and 1/ν 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 differ 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 Deff=1.96(5) (honeycomb), Deff=1.92(4) (Kagome), and Deff=1.83(5) (triangular) for these networks are just compatible to the embedding dimension two.

Magnetization Reversal in Spin Patterns with Complex Geometry

We study field-driven dynamics of spins with antiferromagnetic interactions along the links of a complex substrate geometry, which is modeled by graphs of a controlled connectivity distribution. The magnetization reversal occurs in avalanches of spin flips, which are pinned by the topological constraints of the underlying graph. The hysteresis loop and avalanche sizes are analyzed and classified in terms of the graphs connectivity and clustering. The results are relevant for magnets with a hierarchical spatial inhomogeneity and for design of nanoscale magnetic devices.

Dynamics in Eigen Quasispecies Model

In this work the Eigen model of quasispecies is reconsidered. Our main aim is to find to what extent mutational meltdown changes previously presented results, when the finite population can decrease or increase during evolution.

Simple Cubic Random-Site Percolation Thresholds for Complex Neighbourhoods

In this communication by means of computer simulation we evaluate simple cubic random-site percolation thresholds for neighbourhoods including the nearest neighbours (NN), the next-nearest neighbours (2NN) and the next-next-nearest neighbours (3NN). Our estimations base on finite-size scaling analysis of the percolation probability vs. site occupation probability plots. The Hoshen–Kopelman algorithm has been applied for cluster labelling. The calculated thresholds are 0.1372(1), 0.1420(1), 0.0976(1), 0.1991(1), 0.1036(1), 0.2455(1) for (NN + 2NN), (NN + 3NN), (NN + 2NN + 3NN), 2NN, (2NN + 3NN), 3NN neighbourhoods, respectively. In contrast to the results obtained for a square lattice the calculated percolation thresholds decrease monotonically with the site coordination number z , at least for our inspected neighbourhoods.

Zaller-Deffuant Model of Mass Opinion

Recent formulation of the Zaller model of mass opinion is generalized to include the interaction between agents. The mechanism of interaction is close to the bounded confidence model. The outcome of the simulation is the probability distribution of opinions on a given issue as dependent on the mental capacity of agents. Former result was that a small capacity leads to a strong belief. Here we show that an intensive interaction between agents also leads to a consensus, accepted without doubts.

Bonabeau model on a fully connected graph

Numerical simulations are reported on the Bonabeau model on a fully connected graph, where spatial degrees of freedom are absent. The control parameter is the memory factor f. The phase transition is observed at the dispersion of the agents power h_i. The critical value f_C shows a hysteretic behavior with respect to the initial distribution of h_i. f_C decreases with the system size; this decrease can be compensated by a greater number of fights between a global reduction of the distribution width of h_i. The latter step is equivalent to a partial forgetting.

Avalanches in complex spin networks

We investigate the magnetization reversal processes on classes of complex spin networks with antiferromagnetic interaction along the network links. With slow field ramping the hysteresis loop and avalanches of spin flips occur due to topological inhomogeneity of the network, even without any disorder of the magnetic interaction [B. Tadic, et al., Phys. Rev. Lett. 94 (2005) 137204]. Here we study in detail properties of the magnetization avalanches, hysteresis curves and density of domain walls and show how they can be related to the structural inhomogeneity of the network. The probability distribution of the avalanche size, N_s(s), displays the power-law behaviour for small s, i.e. N_s(s)\propto s^{-\alpha}. For the scale-free networks, grown with preferential attachment, \alpha increases with the connectivity parameter M from 1.38 for M=1 (trees) to 1.52 for M=25. For the exponential networks, \alpha is close to 1.0 in the whole range of M.

Spin-glass properties of an ising antiferromagnet on the archimedean (3,122) lattice

We investigate magnetic properties of a two-dimensional periodic structure with Ising spins and antiferromagnetic nearest neighbor interaction. The structure is topologically equivalent to the Archimedean (3,12^2) lattice. The ground state energy is degenerate. In some ground states, the spin structure is translationally invariant, with the same configuration in each unit cell. Numerical results are reported on specific heat and static magnetic usceptibility against temperature. Both quantities show maxima at temperature T>0. They reveal some sensitivity on the initial state in temperatures where the Edwards--Anderson order parameter is positive. For zero temperature and low frequency of the applied field, the magnetic losses are negligible. However, the magnetization curve displays some erratic behavior due to the metastable states.