Loewner driving functions for off-critical percolation clusters

Details Loewner driving functions for off-critical percolation clusters Loewner driving functions for off-critical percolation clusters

2009-08-10

arxiv.org/abs/0908.1275v2

Phys. Rev. E 80, 050102(R) (2009)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 7 figures

Scientific paper

10.1103/PhysRevE.80.050102

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^{(\nu +1)/2\nu} 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)^\nu, where \nu= 4/3 is the critical exponent for two-dimensional percolation correlation length. The crossover time diverges as (p_c-p)^{-2\nu} as p\to p_c.

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