Bak-Tang-Wiesenfeld model on the square site-percolation lattice (Q2822097)

In this paper, square percolation lattices whose sites are active with probability \(p\) are constructed. It is observed how the geometrical and algebraic properties of the system, such as the fractal dimension of the exterior frontiers of avalanches, gyration radius, loop lengths, cluster masses and Green's function, behave in terms of \(p\). There is a fixed point at \(p=p_c\) which is unstable towards the other fixed point at \(p=1\), which corresponds to the Bak-Tang-Wiesenfeld model. The fractal dimension of the exterior frontier of avalanches at \(p=p_c\) is found to be compatible with the fractal dimension of geometrical spin clusters of the 2D critical Ising model.