Corpus ID: 224802922

Approximate domain Markov property for rigid Ising interfaces

  title={Approximate domain Markov property for rigid Ising interfaces},
  author={Reza Gheissari and Eyal Lubetzky},
  journal={arXiv: Probability},
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

Figures from this paper

Delocalisation and absolute-value-FKG in the solid-on-solid model
The solid-on-solid model is a model of height functions, introduced to study the interface separating the + and − phase in the Ising model. The planar solidon-solid model thus corresponds to theExpand


Tightness and tails of the maximum in 3D Ising interfaces
Consider the 3D Ising model on a box of side length $n$ with minus boundary conditions above the $xy$-plane and plus boundary conditions below it. At low temperatures, Dobrushin (1972) showed thatExpand
Maximum and shape of interfaces in 3D Ising crystals.
Dobrushin (1972) showed that the interface of a 3D Ising model with minus boundary conditions above the $xy$-plane and plus below is rigid (has $O(1)$-fluctuations) at every sufficiently lowExpand
Scaling limit and cube-root fluctuations in SOS surfaces above a wall
Consider the classical $(2+1)$-dimensional Solid-On-Solid model above a hard wall on an $L\times L$ box of $\bbZ^2$. The model describes a crystal surface by assigning a non-negative integer heightExpand
Dynamics of $(2+1)$-dimensional SOS surfaces above a wall: Slow mixing induced by entropic repulsion
We study the Glauber dynamics for the $(2+1)\mathrm{D}$ Solid-On-Solid model above a hard wall and below a far away ceiling, on an $L\times L$ box of $\mathbb{Z}^2$ with zero boundary conditions, atExpand
Harmonic Pinnacles in the Discrete Gaussian Model
The 2D Discrete Gaussian model gives each height function $${\eta : {\mathbb{Z}^2\to\mathbb{Z}}}$$η:Z2→Z a probability proportional to $${\exp(-\beta \mathcal{H}(\eta))}$$exp(-βH(η)), whereExpand
Interface, Surface Tension and Reentrant Pinning Transition in the 2d Ising Model
We develop a new way to look at the high-temperature representation of the Ising model up to the critical temperature and obtain a number of interesting consequences. In the two-dimensional case, itExpand
Ising model in half-space: A series of phase transitions in low magnetic fields
For the Ising model in half-space at low temperatures and for the “unstable boundary condition,” we prove that for each value of the external magnetic field μ, there exists a spin layer of thicknessExpand
Large deviations and continuum limit in the 2D Ising model
Summary. We study the 2D Ising model in a rectangular box ΛL of linear size O(L). We determine the exact asymptotic behaviour of the large deviations of the magnetization ∑t∈ΛLσ(t) when L→∞ forExpand
We investigate the phenomenon of “entropic repulsion” of interfaces in the low temperature Ising model. We study the Gibbs states in the half-space of Z d , d ≥ 3, analogously to the simplifiedExpand
The shape of the (2+1)d SOS surface above a wall
Abstract We give a full description for the shape of the classical ( 2 + 1 ) d Solid-On-Solid model above a wall, introduced by Temperley (1952) [14] . On an L × L box at a large inverse-temperatureExpand