Schramm–Loewner evolution in the three-state Potts model—a numerical study

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Published 9 August 2007 IOP Publishing Ltd
, , Citation Adam Gamsa and John Cardy J. Stat. Mech. (2007) P08020 DOI 10.1088/1742-5468/2007/08/P08020

1742-5468/2007/08/P08020

Abstract

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

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