A violation of the Harris-Barghathi-Vojta criterion

Abstract

In 1974, Harris proposed his celebrated criterion: Continuous phase transitions in $d$-dimensional systems are stable against quenched spatial randomness whenever $d\nu >2$, where $\nu$ is the clean critical exponent of the correlation length. Forty years later, motivated by violations of the Harris criterion for certain lattices such as Voronoi-Delaunay triangulations of random point clouds, Barghathi and Vojta put forth a modified criterion for topologically disordered systems: $a\nu >1$, where $a$ is the disorder decay exponent, which measures how fast coordination number fluctuations decay with increasing length scale. Here we present a topologically disordered lattice with coordination number fluctuations that decay as slowly as those of conventional uncorrelated randomness, but for which the universal behaviour is preserved, hence violating even the modified criterion.

arXiv comment3 pages, 5 figures

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• A non-absorbing SIR stochastic lattice gas model on hybrid lattices
• Fast algorithm for topologically disordered lattices with constant coordination number
• Universality of continuous phase transitions on random Voronoi graphs
• Hyperuniformity in Ashkin-Teller model
• Contact Process on Weighted Planar Stochastic Lattice
• Critical behavior of the stochastic SIR model on random bond-diluted lattices
• Relevance of topological disorder on the directed percolation phase transition
• Harris-Luck criterion in the plateau transition of the Integer Quantum Hall Effect
• Nonuniversal critical dynamics on planar random lattices with heterogeneous degree distributions