Simulation of majority rule disturbed by power-law noise on directed and undirected Barabasi-Albert networks

On directed and undirected Barabasi-Albert networks the Ising model with spin S=1/2 in the presence of a kind of noise is now studied through Monte Carlo simulations. The noise spectrum P(n) follows a power law, where P(n) is the probability of flipping randomly select n spins at each time step. The noise spectrum P(n) is introduced to mimic the self-organized criticality as a model influence of a complex environment. In this model, different from the square lattice, the order-disorder phase transition of the order parameter is not observed. For directed Barabasi-Albert networks the magnetisation tends to zero exponentially and for undirected Barabasi-Albert networks, it remains constant.Comment: 6 pages including many figures, for Int. J. Mod. Phys.

Networks of companies and branches in Poland

In this study we consider relations between companies in Poland taking into account common branches they belong to. It is clear that companies belonging to the same branch compete for similar customers, so the market induces correlations between them. On the other hand two branches can be related by companies acting in both of them. To remove weak, accidental links we shall use a concept of threshold filtering for weighted networks where a link weight corresponds to a number of existing connections (common companies or branches) between a pair of nodes.Comment: 13 pages, 10 figures and 4 table

Ising model spin S=1 on directed Barabasi-Albert networks

On directed Barabasi-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 Barabasi-Albert network.Comment: 8 pages for Int. J. Mod. Phys. C; e-mail: [email protected]

Majority-vote on undirected Barabasi-Albert networks

On Barabasi-Albert networks with z neighbours selected by each added site, the Ising model was seen to show a spontaneous magnetisation. This spontaneous magnetisation was found below a critical temperature which increases logarithmically with system size. 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 and this wasn't found to increase logarithmically with system size. We calculate the value of the critical noise parameter q_c for several values of connectivity $z$ of the undirected Barabasi-Albert network. The critical exponentes beta/nu, gamma/nu and 1/nu were calculated for several values of z.Comment: 15 pages with numerous figure

Self-organized criticality in a model of collective bank bankruptcies

The question we address here is of whether phenomena of collective bankruptcies are related to self-organized criticality. In order to answer it we propose a simple model of banking networks based on the random directed percolation. We study effects of one bank failure on the nucleation of contagion phase in a financial market. We recognize the power law distribution of contagion sizes in 3d- and 4d-networks as an indicator of SOC behavior. The SOC dynamics was not detected in 2d-lattices. The difference between 2d- and 3d- or 4d-systems is explained due to the percolation theory.Comment: For Int. J. Mod. Phys. C 13, No. 3, six pages including four figure

Voter model on Sierpinski fractals

We investigate the ordering of voter model on fractal lattices: Sierpinski Carpets and Sierpinski Gasket. We obtain a power law ordering, similar to the behavior of one-dimensional system, regardless of fractal ramification.Comment: 7 pages, 5 EPS figures, 1 table, uses elsart.cl

A simple model of bank bankruptcies

Interbank deposits (loans and credits) are quite common in banking system all over the world. Such interbank co-operation is profitable for banks but it can also lead to collective financial failures. In this paper we introduce a new model of directed percolation as a simple representation for contagion process and mass bankruptcies in banking systems. Directed connections that are randomly distributed between junctions of bank lattice simulate flows of money in our model. Critical values of a mean density of interbank connections as well as static and dynamic scaling laws for the statistic of avalange bankruptcies are found. Results of computer simulations for the universal profile of bankruptcies spreading are in a qualitative agreement with the third wave of bank suspensions during The Great Depression in the USA.Comment: 8 pages, 6 Encapsulated Postscript figures, to be published in Physica A (2001

Majority-vote on directed Small-World networks

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 in this system. We calculate the value of the critical noise parameter q_c for several values of rewiring probability p of the directed Small-World network. The critical exponentes beta/nu, gamma/nu and 1/nu were calculated for several values of p.Comment: 16 pages including 9 figures, for Int. J. Mod. Phys.

Number of loops of size h in growing scale-free networks

The hierarchical structure of scale-free networks has been investigated focusing on the scaling of the number $N_h(t)$ of loops of size h as a function of the system size. In particular we have found the analytic expression for the scaling of $N_h(t)$ in the Barab\'asi-Albert (BA) scale-free network. We have performed numerical simulations on the scaling law for $N_h(t)$ in the BA network and in other growing scale free networks, such as the bosonic network (BN) and the aging nodes (AN) network. We show that in the bosonic network and in the aging node network the phase transitions in the topology of the network are accompained by a change in the scaling of the number of loops with the system size.Comment: 4 pages, 3 figure

Ferromagnetic Phase Transition in Barabasi-Albert Networks

Ising spins put onto a Barabasi-Albert scale-free network show an effective phase transition from ferromagnetism to paramagnetism upon heating, with an effective critical temperature increasing as the logarithm of the system size. Starting with all spins up and upon equilibration pinning the few most-connected spins down nucleates the phase with most of the spins down.Comment: 8 pages including figure