Crossing probabilities in 2D critical lattice models

Abstract: This talk has two parts. In the first part, we discuss Ising model which is one of the most studied models in statistical physics. We consider critical Ising model in two-dimensional and give crossing probabilities of multiple interfaces in the critical Ising model in polygon with alternating boundary conditions. Similar formulas also hold for other critical lattice models, for instance level lines of discrete Gaussian free field. However, the situation is different when one considers level lines of metric graph Gaussian free field. This leads to the second part of this talk. In the second part, we discuss Gaussian free field (GFF). Discrete GFF and metric graph GFF converge to the same continuum GFF. However, their crossing probabilities are distinct. We will explain the difference and show how to calculate them.

Mathematics

Audience: researchers in the topic

ICCM 2020