Ising Interfaces and Free Boundary Conditions

TL;DR

This paper demonstrates that the interfaces in the 2D critical Ising model with free boundary conditions converge to dipolar SLE(3), extending previous results and confirming a conjecture in the field.

Contribution

It proves that Ising model interfaces with free boundary conditions converge to dipolar SLE(3), generalizing earlier work and confirming a key conjecture.

Findings

Interfaces converge to dipolar SLE(3) at criticality

Generalizes previous SLE interface results

Confirms a conjecture of Bauer, Bernard, and Houdayer

Abstract

We study the interfaces arising in the two-dimensional Ising model at critical temperature, without magnetic field. We show that in the presence of free boundary conditions between plus and minus spins, the scaling limit of these interfaces can be described by a variant of SLE, called dipolar SLE(3). This generalizes a celebrated result of Chelkak and Smirnov and proves a conjecture of Bauer, Bernard and Houdayer. We mention two possible applications of our result.