Percolation Crossing Formulas and Conformal Field Theory

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dc.creatorSimmons, Jacob J. H.
dc.creatorKleban, Peter
dc.creatorZiff, Robert M.
dc.date2007-05-14
dc.date2007-06-03
dc.date.accessioned2026-07-07T10:35:51Z
dc.date.available2026-07-07T10:35:51Z
dc.descriptionUsing conformal field theory, we derive several new crossing formulas at the two-dimensional percolation point. High-precision simulation confirms these results. Integrating them gives a unified derivation of Cardy's formula for the horizontal crossing probability $Π_h(r)$, Watts' formula for the horizontal-vertical crossing probability $Π_{hv}(r)$, and Cardy's formula for the expected number of clusters crossing horizontally $\mathcal{N}_h(r)$. The main step in our approach implies the identification of the derivative of one primary operator with another. We present operator identities that support this idea and suggest the presence of additional symmetry in $c=0$ conformal field theories.
dc.description12 pages, 5 figures. Numerics improved; minor corrections
dc.identifierhttps://arxiv.org/abs/0705.1933
dc.identifierhttp://arxiv.org/abs/0705.1933
dc.identifierJ.Phys.A40:F771,2007
dc.identifierdoi:10.1088/1751-8113/40/31/F03
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/179864
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectProbability
dc.titlePercolation Crossing Formulas and Conformal Field Theory
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