Critical properties of island perimeters in the flooding transition of stochastic and rotational sandpile models

Critical properties of external perimeters of islands that appear at the flooding transition in the toppling surfaces, defined by the toppling number Si of each sand column, of stochastic and rotational sandpile models are studied. A set of new critical exponents are estimated by extensive numerical simulation and finite size scaling analysis. The values of the critical exponents are found different for these sandpile models. Several scaling relations among the critical exponents and the Hurst exponent describing the self-affinity of the toppling surfaces are established and verified. The critical exponents obtained here are also found connected to the exponents describing the avalanche size distribution.