6 research outputs found
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
A Biased Review of Sociophysics
Various aspects of recent sociophysics research are shortly reviewed:
Schelling model as an example for lack of interdisciplinary cooperation,
opinion dynamics, combat, and citation statistics as an example for strong
interdisciplinarity.Comment: 16 pages for J. Stat. Phys. including 2 figures and numerous
reference