Loewner driving functions for off-critical percolation clusters

Yoichiro Kondo, Namiko Mitarai, Hiizu Nakanishi

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Article number050102
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
Publication statusPublished - Nov 4 2009

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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