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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.

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