English

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

Statistical Mechanics 2007-08-14 v2 Mathematical Physics math.MP

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.

Cite

@article{arxiv.0705.1510,
  title  = {SLE in the three-state Potts model - a numerical study},
  author = {Adam Gamsa and John Cardy},
  journal= {arXiv preprint arXiv:0705.1510},
  year   = {2007}
}
R2 v1 2026-06-21T08:27:07.208Z