2024/11/25 by Léonie Papon, Papon, Léonie
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2411.16452
openalex publication_date 2024/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the interface separating +1 and -1 spins in the critical planar Ising model with Dobrushin boundary conditions perturbed by an external magnetic field has a scaling limit. This result holds when the Ising model is defined on a bounded and simply connected subgraph of δℤ2, with δ>0. We show that if the scaling of the external field is of order δ15/8, then, as δ→ 0, the interface converges in law to a random curve whose law is conformally covariant and absolutely continuous with respect to SLE3. This limiting law is a massive version of SLE3 in the sense of Makarov and Smirnov and we give an explicit expression for its Radon-Nikodym derivative with respect to SLE3. We also prove that if the scaling of the external field is of order δ15/8g1(δ) with g1(δ)→ 0, then the interface converges in law to SLE3. In contrast, we show that if the scaling of the external field is of order δ15/8g2(δ) with g2(δ) → ∞, then the interface degenerates to a boundary arc.