Self-organizing height-arrow model: numerical and analytical results

The recently introduced self-organizing height-arrow (HA) model is studied numerically on the square lattice and analytically on the Bethe lattice. The concentration of occupied sites and critical exponents of distributions of avalanches are evaluated for two slightly different versions of the model. The exponents found for distributions of avalanches by mass, area, duration and appropriate fractal dimensions are close to those for the original sandpile model, which suggests that the HA model belongs to the same universality class. For comparison, the concentration of occupied sites in the HA model is calculated exactly on the Bethe lattice with coordination number q=4.