Dresden 2011 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 42: Critical Phenomena and Phase Transitions
DY 42.3: Talk
Friday, March 18, 2011, 10:45–11:00, ZEU 255
Migdal-Kadanoff approximation to the diluted negative-weight percolation problem — •Oliver Melchert1, Stefan Boettcher2, and Alexander K. Hartmann1 — 1Institut für Physik, Carl-von-Ossietzky Universität Oldenburg, Oldenburg (Germany) — 2Department of Physics, Emory University, Atlanta (USA)
We consider the diluted negative weight percolation (NWP) problem [1] on lattice graphs, wherein edge weights are drawn from disorder distributions that allow for weights of either sign. We are interested whether there are system-spanning paths or loops of total negative weight. So as to study the model on hypercubic lattice graphs numerically, one has to perform a non-trivial transformation of the original graph and apply sophisticated matching algorithms.
Here, we consider the NWP model on hierarchical lattice graphs,
where a Migdal-Kadanoff (MK) approximation can be used to gain insight on the topology of the
phase diagram. For a very basic disorder distribution we set up a renormalization group (RG)
transformation and study the RG flow in the disorder-dilution plane in order
to find fixed points and critical indices for the linearized model.
We further implement the “pool” method [2] to yield the phase diagram and critical
exponents upon decimation of huge graphs and we compare our findings to
previous results from finite-size scaling analyses [1,3].
[1] L. Apolo, OM, and A.K. Hartmann, Phys. Rev. E 79 (2009) 031103
S. Boettcher, Eur. Phys. J. B 33 (2003) 439
OM, L. Apolo, and A.K. Hartmann, Phys. Rev. E 81 (2010) 051108