Loewner driving functions for off-critical percolation clusters.
We numerically study the Loewner driving function Ut of a site percolation cluster boundary on the triangular lattice for p<pc . It is found that Ut shows a drifted random walk with a finite crossover time. Within this crossover time, the averaged driving function Ut shows a scaling behavior -(pc-p)t(nu+1)/2nu with a superdiffusive fluctuation whereas, beyond the crossover time, the driving function Ut undergoes a normal diffusion with Hurst exponent 1/2 but with the drift velocity proportional to (pc-p)nu , where nu=4/3 is the critical exponent for two-dimensional percolation correlation length. The crossover time diverges as (pc-p)-2nu as p-->pc.
Kondo
Yoichiro
Y
Department of Physics, Kyushu University, 33, Fukuoka 812-8581, Japan. ykondo@stat.phys.kyushu-u.ac.jp
Mitarai
Namiko
N
Nakanishi
Hiizu
H
D000465:Algorithms; D003198:Computer Simulation; D004058:Diffusion; D008956:Models, Chemical; D015233:Models, Statistical; D044367:Phase Transition