SLE in the three-state Potts model - a numerical study

Abstract

The scaling limit of the spin cluster boundaries of the Ising model with domain wall boundary conditions is SLE with kappa=3. We hypothesise that the three-state Potts model with appropriate boundary conditions has spin cluster boundaries which are also SLE in the scaling limit, but with kappa=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.

32 pages, 41 figures

References in corpus (3)

• SLE for theoretical physicists
• 2D growth processes: SLE and Loewner chains
• The scaling limit of two cluster boundaries in critical lattice models

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