arXiv subjects

Daniel Tiggemann

Publications and source records attributed to Daniel Tiggemann.

3 recordsLinked to original sources

arXiv2006

Percolation on Growing Lattices

In order to investigate the dependence on lattice size of several observables in percolation, the Hoshen-Kopelman algorithm was modified so that growing lattices could be simulated. By this way, when simulating a lattice of size L, lattices of smaller sizes can be simulated in the same run for free, saving computing time. Here, site percolation in three dimensions was studied. Lattices of up to L=5000, with many L-steps in between, have been simulated, for occupation probabilities of p=0.25, p=0.3, p=p_c=0.311608, and p=0.35.

cond-mat.stat-mech↗

arXiv2004

New results for the dynamical critical behaviour of the two-dimensional Ising model

Using the new supercomputer JUMP at the Research Center Juelich, we were able to simulate large lattices (up to L=2000000, meaning a new world record) for long times (up to T=6000 for L=150000). Using this data, we examined the dynamical critical exponent z. The old assumption of z=2 with logarithmic corrections seems very unlikely according to our data, leaving the asymptotic value of z~=2.167.

cond-mat.stat-mech↗

arXiv2001

Simulation of percolation on massively-parallel computers

A novel approach to parallelize the well-known Hoshen-Kopelman algorithm has been chosen, suitable for simulating huge lattices in high dimensions on massively-parallel computers with distributed memory and message passing. This method consists of domain decomposition of the simulated lattice into strips perpendicular to the hyperplane of investigation that is used in the Hoshen-Kopelman algorithm. Systems of world record sizes, up to L=4000256 in two dimensions, L=20224 in three, and L=1036 in four, gave precise estimates for the Fisher exponent tau, the corrections to scaling Delta_1, and for the critical number density n_c.

cond-mat.stat-mech↗