Percolation of fully penetrable disks using the three-leg cluster method

The three-leg cluster method is a relatively new approach to computing the percolation thresholds. To date, it has only been applied to lattice models. It is characterized by high versatility in choosing the shape of the system and by the universal probability $1/2$ that, at the phase transition, a three-leg cluster exists that spans three segments of the system border. We applied it to the problem of continuous percolation of discs, for which we estimated the critical filling factor to be $1.128~086~7(5)$ . This confirms that the three-leg cluster method is applicable to continuous percolation models.