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At the critical point in two dimensions, the number of percolation clusters of enclosed area greater than A is proportional to A−1, with a proportionality constant C that is universal. We show theoretically (based upon Coulomb gas methods), and verify numerically to high precision, that $$C = 1/(8\sqrt 3 \pi = 0.022972037 \ldots )$$ . We also derive, and verify to varying precision, the corresponding...
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