QLunch: Boris Bolvig Kjær

Speaker: Boris Bolvig Kjær from QMATH

Title: Percolation and the loop O(1) model

Abstract: 

After much success in using the double random current representation in the study of the Ising model, Duminil-Copin posed the question in 2016 of determining the phase transition of the single random current. By relating to the loop O(1) model on $\mathbb{Z}^d$ we exhibit a phase transition in which the size of clusters of the model corresponding to a super-critical Ising model have infinite expectation.

In this talk I will gently introduce graphical representations of the Ising model and motivate the theory of percolation followed by a discussion of new results whose surprising proof takes inspiration from the toric code in quantum theory.

Based on joint work with Ulrik Tinggaard Hansen and Frederik Ravn Klausen: https://arxiv.org/abs/2306.05130.