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Proposal for a CFT interpretation of Watts' differential equation for percolation

Michael A. I. Flohr·Annekathrin Mueller-Lohmann
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Abstract

G. M. T. Watts derived that in two dimensional critical percolation the crossing probability Pi_hv satisfies a fifth order differential equation which includes another one of third order whose independent solutions describe the physically relevant quantities 1, Pi_h, Pi_hv. We will show that this differential equation can be derived from a level three null vector condition of a rational c=-24 CFT and motivate how this solution may be fitted into known properties of percolation.

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Michael A. I. Flohr, Annekathrin Mueller-Lohmann. 2005-11-21. Proposal for a CFT interpretation of Watts' differential equation for percolation. https://doi.org/10.1088/1742-5468%2F2005%2F12%2Fp12004

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