The effects of disorder on Harris-criterion violating percolation

Quantum and classical localization in the lowest Landau level

Spatial correlations of occupation probabilities, if their decay is not too fast, can change the critical exponents for classical percolation. From numerical studies of electron dynamics in the lowest Landau level (LLL) we demonstrate the quantum analog of this effect. Similar to classical percolation, we find that the extended Harris criterion applies to localization in the LLL. These results suggest experiments that might probe new quantum critical points in the integer quantum Hall setting.

非周期、拓扑及非关联无序下干净临界点稳定性的数值研究

Numerical Study of Stability of Clean Critical Points across Aperiodic, Topological, and Uncorrelated Disorder

本研究通过二维Ashkin-Teller模型数值比较三种非周期晶格的临界行为，发现稀释晶格破坏干净普适性，而Smith-hat平铺和VD三角剖分保持干净AT普适类，验证了HBV判据优于Harris判据。

Critical Exponents for Diluted Resistor Networks

An approach by Stephen is used to investigate the critical properties of randomly diluted resistor networks near the percolation threshold by means of renormalized field theory. We reformulate an existing field theory by Harris and Lubensky. By a decomposition of the principal Feynman diagrams we obtain a type of diagrams which again can be interpreted as resistor networks. This new interpretation provides for an alternative way of evaluating the Feynman diagrams for random resistor networks. We calculate the resistance crossover exponent $ϕ$ up to second order in $ε=6-d$, where $d$ is the spa…

Violating conformal invariance: Two-dimensional clusters grafted to wedges, cones, and branch points of Riemann surfaces

We present simulations of 2-d site animals on square and triangular lattices in non-trivial geomeLattice animals are one of the few critical models in statistical mechanics violating conformal invariance. We present here simulations of 2-d site animals on square and triangular lattices in non-trivial geometries. The simulations are done with the newly developed PERM algorithm which gives very precise estimates of the partition sum, yielding precise values for the entropic exponent $θ$ ($Z_N \sim μ^N N^{-θ}$). In particular, we studied animals grafted to the tips of wedges with a wide range of …

Effects of lattice dilution on the non-equilibrium phase transition in the stochastic Susceptible-Infectious-Recovered model

We investigate how site dilution, as would be introduced by immunization, affects the properties of the active-to-absorbing non-equilibrium phase transition in the paradigmatic Susceptible-Infectious-Recovered (SIR) model on regular cubic lattices. According to the Harris criterion, the critical behavior of the SIR model, which is governed by the universal scaling exponents of the dynamic isotropic percolation (DyIP) universality class, should remain unaltered after introducing impurities. However, when the SIR reactions are simulated for immobile agents on two- and three-dimensional lattices …