Abstract
The scaling limit of the spin cluster boundaries of the Ising model withdomain wall boundary conditions is Schramm–Loewner evolution (SLE) withκ = 3. We hypothesize that the three-state Potts model with appropriate boundary conditionshas spin cluster boundaries which are also SLE in the scaling limit, but withκ = 10/3. To test this, we generate samples using the Wolff algorithm and test them againstpredictions of SLE: we examine the statistics of the Loewner driving function, estimate thefractal dimension and test against Schramm’s formula. The results are in support of ourhypothesis.
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