Abstract
A renormalisation group approach to two-dimensional percolation problems on the honeycomb lattice (bond) and the Kagome lattice (site and bond) is developed using a scaling transformation in real space. A finite cluster approach, called the electrode method, gives the location of the fixed point p*, the eigenvalue lambda and the correlation length critical exponent nu ; the results are p*=0.6308, lambda =1.669 and nu =1.353 for both the honeycomb lattice (bond) and the Kagome lattice (site), and p*=0.4697, lambda =1.577 and nu =1.522 for the Kagome lattice (bond). The fixed point p* for the honeycomb lattice (bond) and the Kagome lattice (site) is in good agreement with the exact critical percolation probability obtained by Sykes and Essam (1964).
Published Version
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