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 (ν+1) /2ν 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) ν, where ν=4/3 is the critical exponent for two-dimensional percolation correlation length. The crossover time diverges as (pc -p) -2ν as p→ pc.