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Loop content of bond percolation on hyperbolic triangulations: an exact identity and a $1/λ$ expansion

Treisman, Zachary
arXiv (All) · Papers
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probabilitystatistical-mechanics
We study the homology of percolation clusters on disk-shaped patches of the regular $\{3,q\}$ triangle tilings for $q\ge7$. Varying $q$ gives a one-parameter family of hyperbolic tilings, from mildly curved ($q=7$) to deeply hyperbolic ($q=20$), and this paper measures and derives loop content as a
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