The shape of two-dimensional percolation and Ising clusters

The authors compute numerically the asphericity of (i) percolation clusters at the percolation concentration on a square lattice, and (ii) Ising clusters at the critical temperature of an Ising model, also on a square lattice. These results are compared with various analytical calculations. For the percolation problem, they also compute the distribution of asphericities among different clusters. Finally, they show that the lattice itself does not give rise to any anisotropy.