43 research outputs found
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
Test of Universality in Anisotropic 3D Ising Model
Chen and Dohm predicted theoretically in 2004 that the widely believed
universality principle is violated in the Ising model on the simple cubic
lattice with more than only six nearest neighbours. Schulte and Drope by Monte
Carlo simulations found such violation, but not in the predicted direction.
Selke and Shchur tested the square lattice. Here we check only this
universality for the susceptibility ratio near the critical point. For this
purpose we study first the standard Ising model on a simple cubic lattice with
six nearest neighbours, then with six nearest and twelve next-nearest
neighbours, and compare the results with the Chen-Dohm lattice of six nearest
neighbours and only half of the twelve next-nearest neighbours. We do not
confirm the violation of universality found by Schulte and Drope in the
susceptibility ratio.Comment: 6 pages including 4 figures, Physica A, in pres
Ising model with spins S=1/2 and 1 on directed and undirected Erd\"os-R\'enyi random graphs
Using Monte Carlo simulations we study the Ising model with spin S=1/2 and 1
on {\it directed} and {\it undirected} Erd\"os-R\'enyi (ER) random graphs, with
neighbors for each spin. In the case with spin S=1/2, the {\it undirected}
and {\it directed} ER graphs present a spontaneous magnetization in the
universality class of mean field theory, where in both {\it directed} and {\it
undirected} ER graphs the model presents a spontaneous magnetization at (), but no spontaneous magnetization at which is
the percolation threshold. For both {\it directed} and {\it undirected} ER
graphs with spin S=1 we find a first-order phase transition for z=4 and 9
neighbors.Comment: 11 pages, 8 figure
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 simulation in directed lattices and networks
On directed lattices, with half as many neighbours as in the usual undirected
lattices, the Ising model does not seem to show a spontaneous magnetisation, at
least for lower dimensions. Instead, the decay time for flipping of the
magnetisation follows an Arrhenius law on the square and simple cubic lattice.
On directed Barabasi-Albert networks with two and seven neighbours selected by
each added site, Metropolis and Glauber algorithms give similar results, while
for Wolff cluster flipping the magnetisation decays exponentially with time.Comment: Expanded to 8 pages: additional author, additional result
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