Author: | D. Tiggemann. |

Published as: | Diploma thesis at the Institute for Theoretical Physics at the University of Cologne. |

Abstract: |
Within this diploma thesis, a novel approach to parallelizing 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 consisted of domain decomposition
of the simulated lattice into strips perpendicular to the hyperplane of
investigation that is used in the Hoshen-Kopelman algorithm. This approach
is more complicated than others, but it allows for simulating
huge lattices, even in dimensions above two.
Using the parallelized algorithm, it was possible to simulate random site percolation on the square (resp. cubic and hypercubic) lattice in two, three, and four dimensions, with maximum lattice sizes of L=4000256 (2d), L=20224 (3d), and L=1036 (4d). These are the largest systems percolation was ever simulated on, thus yielding three world records. All simulations were done on the very fast Cray T3E at the Research Center Jülich. Using the data generated with the world record simulations, it was possible to investigate some properties of percolation with high precision, i. e. critical exponents like the Fisher exponent tau or the corrections
to scaling exponent Delta, and the number density at the critical point
_{1}n. Comparison with values obtained by other groups with other methods
were in reasonable agreement.
_{c} |

PDF-Source: | http://www.thp.uni-koeln.de/~dt/papers/2001/dipl/thesis.pdf (85 pages, 414 KByte). |

PS-Source: | http://www.thp.uni-koeln.de/~dt/papers/2001/dipl/thesis.ps (85 pages, 475 KByte). |