Particle–hole symmetry in a sandpile model

In a sandpile model addition of a hole is defined as the removal of a grain from the sandpile. We show that hole avalanches can be defined very similarly to particle avalanches. A combined particle–hole sandpile model is then defined where particle avalanches are created with probability p and hole avalanches are created with the probability 1−p. It is observed that the system is critical with respect to either particle or hole avalanches for all values of p except at the symmetric point of pc = 1/2. However, at pc the fluctuating mass density has non-trivial correlations characterized by a 1/f type of power spectrum.