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

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

2007-05-10

arxiv.org/abs/0705.1510v2

Adam Gamsa et al J. Stat. Mech. (2007) P08020

Physics

Condensed Matter

Statistical Mechanics

32 pages, 41 figures

Scientific paper

10.1088/1742-5468/2007/08/P08020

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.

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