2009/07/31 by M. Caselle, M Caselle, S. Lottini +3
Mathematics · Physics and Astronomy · #Quantum many-body systems #Random Matrices and Applications #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1088/1742-5468/2011/02/p02039
published as J.Stat.Mech.1102:P02039,2011 · Final version published in JSTAT. 13 pages, 5 figures. Substantial changes in the data production, analysis and in the conclusions. Added a section about the crossing probability. Typeset with 'iopart'
arxiv created 2011/02/28 · openalex publication_date 2011/02/28 · arxiv updated 2011/03/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We study the fractal properties of interfaces in the 2d Ashkin–Teller model. The fractal dimension of the symmetric interfaces is calculated along the critical line of the model in the interval between the Ising and the four-states Potts models. Using Schramm's formula for crossing probabilities we show that such interfaces cannot be related to the simple SLE κ , except for the Ising point. The same calculation on non-symmetric interfaces is performed in the four-states Potts model: the fractal dimension is compatible with the result coming from Schramm's formula, and we expect a simple SLE κ in this case.