Corpus ID: 224802922

Approximate domain Markov property for rigid Ising interfaces

@article{Gheissari2020ApproximateDM,
  title={Approximate domain Markov property for rigid Ising interfaces},
  author={Reza Gheissari and Eyal Lubetzky},
  journal={arXiv: Probability},
  year={2020}
}
Consider the Ising model on a centered box of side length $n$ in $\mathbb Z^d$ with $\mp$-boundary conditions that are minus in the upper half-space and plus in the lower half-space. Dobrushin famously showed that in dimensions $d\ge 3$, at low-temperatures the Ising interface (dual-surface separating the plus/minus phases) is rigid, i.e., it has $O(1)$ height fluctuations. Recently, the authors decomposed these oscillations into pillars and identified their typical shape, leading to a law of… Expand

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