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The site percolation threshold of the square lattice
Find a closed form for the site percolation threshold of the square lattice, p_c ≈ 0.5927460508; bond percolation has p_c = 1/2.
| 1 | { |
| 2 | "domain": "physics-astronomy", |
| 3 | "topics": [ |
| 4 | "statistical-mechanics", |
| 5 | "probability" |
| 6 | ], |
| 7 | "type": "construction", |
| 8 | "source": { |
| 9 | "key": "horizonmath", |
| 10 | "name": "HorizonMath", |
| 11 | "url": "https://github.com/ewang26/HorizonMath/blob/4ef0b61a8a6d4c5ded661fab7c2e896af84abe6e/data/problems_full.json#L781-L791", |
| 12 | "id": "site_percolation_square", |
| 13 | "curator": "Erik Y. Wang, Sumeet R. Motwani et al.", |
| 14 | "status": "open", |
| 15 | "as_of": "2026-10-20", |
| 16 | "catalog": "0521c19bbd38" |
| 17 | } |
| 18 | } |