2007/05/31 by Adam Gamsa, John Cardy · 2 citations
Mathematics · Physics and Astronomy · #Boundary (topology) #Boundary value problem #Chiral Potts curve #Domain (mathematical analysis) #Ising model #Limit (mathematics) #Opinion Dynamics and Social Influence #Potts model #Quantum many-body systems #Scaling #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1088/1742-5468/2007/08/p08020
published as Adam Gamsa et al J. Stat. Mech. (2007) P08020 · 32 pages, 41 figures
openalex publication_date 2007/08/09 · arxiv created 2007/08/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The scaling limit of the spin cluster boundaries of the Ising model with domain wall boundary conditions is Schramm–Loewner evolution (SLE) with κ = 3. We hypothesize that the three-state Potts model with appropriate boundary conditions has spin cluster boundaries which are also SLE in the scaling limit, but with κ = 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.