Proposal for a CFT interpretation of Watts' differential equation for percolation
High Energy Physics - Theory
2011-02-16 v2 Statistical Mechanics
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.hep-th/0507211,
title = {Proposal for a CFT interpretation of Watts' differential equation for percolation},
author = {Michael A. I. Flohr and Annekathrin Mueller-Lohmann},
journal= {arXiv preprint arXiv:hep-th/0507211},
year = {2011}
}
Comments
LaTeX, 20p, added references, corrected typos and additional contents