Continuity of the phase transition in Ising models

Jakob Bjørnberg, Chalmers Göteborg

The Ising model is a one of the most studied models for phase transition. Most famous is its classical formulation, and there is also a quantum version called the transverse field Ising model. Here we consider the question of continuity of the phase transition in these models. In 2013 Aizenman, Duminil-Copin and Sidoravicius proved continuity in the final missing case d=3 for the classical model defined on the lattice $\ZZ^d$.  Similar arguments can be used to show continuity of the phase transition also in the quantum model. We give an outline of the argument in this talk. Interestingly, the main part of the argument is probabilistic and uses a graphical representation.