The Harris-Luck criterion for random lattices

Details The Harris-Luck criterion for random lattices The Harris-Luck criterion for random lattices

2003-10-12

arxiv.org/abs/cond-mat/0310269v2

Phys.Rev.B69:144208,2004

Physics

Condensed Matter

Statistical Mechanics

13 pages, 9 figures, 2 tables, REVTeX 4. Version as published, one figure added for clarification, minor re-wordings and typo

Scientific paper

10.1103/PhysRevB.69.144208

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 matter 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 Voronoi-Delaunay construction and of planar, ``fat'' $\phi^3$ 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.

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