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}
}