Regensburg 2004 – scientific programme
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DY: Dynamik und Statistische Physik
DY 16: Phase Transitions
DY 16.3: Talk
Monday, March 8, 2004, 17:15–17:30, H2
The Harris-Luck Criterion for Random Lattices — •Wolfhard Janke and Martin Weigel — Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, 04109 Leipzig, Germany
The Harris-Luck criterion judges the relevance of (potentially) spatially
correlated, quenched disorder induced by, e.g., random bonds, randomly
diluted
sites or a quasi-periodicity of the lattice, for altering the critical
behavior of
a coupled statistical mechanics system. We investigate the applicability of
this type of criterion
to the case of spin variables coupled to random lattices. Their
aptitude to
alter critical behavior depends on the degree of spatial correlations
present,
which is quantified by a wandering exponent. We consider the cases
of
Poissonian random graphs resulting from the Voronoï-Delaunay
construction and of
planar, “fat” φ3 Feynman diagrams and precisely determine their
wandering
exponents. The resulting predictions are compared to various exact and
numerical
results for the Potts model coupled to these quenched ensembles of random
graphs.
[1] W. Janke and M. Weigel, The Harris-Luck criterion for random lattices,
Leipzig preprint LU-ITP 2003/021, e-print cond-mat/0310269.