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arXiv · 0908.1275

Loewner driving functions for off-critical percolation clusters

Yoichiro Kondo·Namiko Mitarai·Hiizu Nakanishi
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Abstract

We numerically study the Loewner driving function U_t of a site percolation cluster boundary on the triangular lattice for p shows a scaling behavior -(p_c-p) t^{(ν+1)/2ν} with a superdiffusive fluctuation whereas, beyond the crossover time, the driving function U_t undergoes a normal diffusion with Hurst exponent 1/2 but with the drift velocity proportional to (p_c-p)^ν, where ν= 4/3 is the critical exponent for two-dimensional percolation correlation length. The crossover time diverges as (p_c-p)^{-2ν} as p\to p_c.

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Yoichiro Kondo, Namiko Mitarai, Hiizu Nakanishi. 2009-11-08. Loewner driving functions for off-critical percolation clusters. https://doi.org/10.1103/physreve.80.050102

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