Phase transitions in statistical mechanics - The Ising model and beyondCRC 1720: Early Career Seminar

by Max Mihailescu

Tuesday Jun 23, 2026, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

In this talk, we will look at a class of discrete models from statistical mechanics, with a focus on phase transitions. As a model for ferro-magnetism, the Ising model has extensively been studied in the last 90 years. Even with its simple formulation it offers a large range of phenomena. One of its key features is that its behavior depends strongly on the temperature regime. At high temperatures, typical configurations are disordered, corresponding to non-magnetized materials in the real world. In contrast, at low temperatures, spins are very strongly correlated over long distances. In the first half of the talk I will review the mathematical framework as well as some classical results. The second half will focus on recent work, where we consider a class of models that are related to the Ising model, but which do not undergo a phase transition. The proof goes by translating observables of the spin system to connectivity events in a certain percolation model.