Berlin 2012 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 31: Phase Transitions and Critical Phenomena
DY 31.3: Talk
Friday, March 30, 2012, 10:15–10:30, MA 004
Mean-field behavior of the negative-weight percolation model on random regular graphs — •Oliver Melchert1, Alexander K. Hartmann1, and Marc Mezard2 — 1Institut für Physik, Universität Oldenburg (Germany) — 2Laboratoire de Physique Théorique et Modeles Statistiques, Université de Paris Sud (France)
In the presented study, we investigate the critical properties of minimum-weight loops and
paths in the negative-weight percolation
(NWP) problem on 3-regular random graphs (RRGs), i.e. graphs
where each node has exactly 3 neighbors and were there is no regular
lattice structure [1].
By studying a particular model on RRGs, one has direct access to the
mean-field exponents that govern the model for d>du.
The presented study aims to support the previous conjecture
du=6 [2] by directly computing the mean field exponents for the NWP model with
a bimodal weight distribution, and comparing
them to those found for a regular hypercubic lattice with dimension d=6.
The presented results are obtained via computer simulations, using an appropriate
mapping to a matching problem, as well as by
analytic means, using the replica symmetric cavity method for a related polymer problem.
We find that the numerical values for the critical exponents on RRGs agree
with those found for d=6-dimensional hypercubic lattice graphs within errorbars and hence support
the conjectured upper critical dimension du=6.
OM, A.K. Hartmann, and M. Mézard, PRE 84, 041106 (2011)
OM, L. Apolo, and A.K. Hartmann, PRE 81, 051108 (2010)