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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.
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| 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 | +} | |