Geometrical properties of parafermionic spin models
Abstract
We present measurements of the fractal dimensions associated to the geometrical clusters for Z4 and Z5 spin models. We also attempted to measure similar fractal dimensions for the generalised Fortuyin Kastelyn (FK) clusters in these models but we discovered that these clusters do not percolate at the critical point of the model under consideration. These results clearly mark a difference in the behaviour of these non local objects compared to the Ising model or the 3-state Potts model which corresponds to the simplest cases of ZN spin models with N=2 and N=3 respectively. We compare these fractal dimensions with the ones obtained for SLE interfaces.
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