Non-Universality in Semi-Directed Barabasi-Albert Networks

In usual scale-free networks of Barabasi-Albert type, a newly added node selects randomly m neighbors from the already existing network nodes, proportionally to the number of links these had before. Then the number N(k) of nodes with k links each decays as 1/k^gamma where gamma=3 is universal, i.e. independent of m. Now we use a limited directedness in the construction of the network, as a result of which the exponent gamma decreases from 3 to 2 for increasing m.Comment: 5 pages including 2 figures and computer progra

Monte Carlo simulation of Ising model on directed Barabasi-Albert network

The existence of spontaneous magnetization of Ising spins on directed Barabasi-Albert networks is investigated with seven neighbors, by using Monte Carlo simulations. In large systems we see the magnetization for different temperatures T to decay after a characteristic time tau, which is extrapolated to diverge at zero temperature.Comment: Error corrected, main conclusion unchanged; for Int. J. Mod. Phys. C 16, issue 4 (2005

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]

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.

Comparison of Ising magnet on directed versus undirected Erdos-Renyi and scale-free network

Scale-free networks are a recently developed approach to model the interactions found in complex natural and man-made systems. Such networks exhibit a power-law distribution of node link (degree) frequencies n(k) in which a small number of highly connected nodes predominate over a much greater number of sparsely connected ones. In contrast, in an Erdos-Renyi network each of N sites is connected to every site with a low probability p (of the orde r of 1/N). Then the number k of neighbors will fluctuate according to a Poisson distribution. One can instead assume that each site selects exactly k neighbors among the other sites. Here we compare in both cases the usual network with the directed network, when site A selects site B as a neighbor, and then B influences A but A does not influence B. As we change from undirected to directed scale-free networks, the spontaneous magnetization vanishes after an equilibration time following an Arrhenius law, while the directed ER networks have a positive Curie temperature.Comment: 10 pages including all figures, for Int. J, Mod. Phys. C 1

Reexamination of scaling in the five-dimensional Ising model

In three dimensions, or more generally, below the upper critical dimension, scaling laws for critical phenomena seem well understood, for both infinite and for finite systems. Above the upper critical dimension of four, finite-size scaling is more difficult. Chen and Dohm predicted deviation in the universality of the Binder cumulants for three dimensions and more for the Ising model. This deviation occurs if the critical point T = Tc is approached along lines of constant A = L*L*(T-Tc)/Tc, then different exponents a function of system size L are found depending on whether this constant A is taken as positive, zero, or negative. This effect was confirmed by Monte Carlo simulations with Glauber and Creutz kinetics. Because of the importance of this effect and the unclear situation in the analogous percolation problem, we here reexamine the five-dimensional Glauber kinetics.Comment: 8 pages including 5 figure

Highly Nonlinear Ising Model and Social Segregation

The usual interaction energy of the random field Ising model in statistical physics is modified by complementing the random field by added to the energy of the usual Ising model a nonlinear term S^n were S is the sum of the neighbor spins, and n=0,1,3,5,7,9,11. Within the Schelling model of urban segregation, this modification corresponds to housing prices depending on the immediate neighborhood. Simulations at different temperatures, lattice size, magnetic field, number of neighbors and different time intervals showed that results for all n are similar, expect for n=3 in violation of the universality principle and the law of corresponding states. In order to find the critical temperatures, for large n we no longer start with all spins parallel but instead with a random configuration, in order to facilitate spin flips. However, in all cases we have a Curie temperature with phase separation or long-range segregation only below this Curie temperature, and it is approximated by a simple formula: Tc is proportional to 1+m for n=1, while Tc is roughly proportional to m for n >> 1.Comment: 10 pages including many figure

Simulation of Demographic Change in Palestinian Territories

Mortality, birth rates and retirement play a major role in demographic changes. In most cases, mortality rates decreased in the past century without noticeable decrease in fertility rates, this leads to a significant increase in population growth. In many poor countries like Palestinian territories the number of births has fallen and the life expectancy increased. In this article we concentrate on measuring, analyzing and extrapolating the age structure in Palestine a few decades ago into future. A Fortran program has been designed and used for the simulation and analysis of our statistical data. This study of demographic change in Palestine has shown that Palestinians will have in future problems as the strongest age cohorts are the above-60-year olds. We therefore recommend the increase of both the retirement age and women employment.Comment: For Int. J. Mod. Phys. C 18, issue 11; 9 pages including figures and progra

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.