“Critical and near-critical scaling limits for the planar Ising model”
Venerdì 6 Novembre 2020, ore 14:00 - Zoom - Federico Camia (NYU Abu Dhabi)
The Ising model, proposed by Lenz in 1920 to describe ferromagnetism, is one the most studied models of statistical mechanics. Its two dimensional version has played a special role in rigorous statistical mechanics since Peierls’ proof of a phase transition in 1936 and Onsager’s derivation of the free energy in 1944. This continues to be the case today, thanks to new results on the continuum scaling limit. In this talk, I will first introduce the model and give a brief historical overview of some milestones in its analysis. I will then present recent results on its critical and near-critical scaling limits, focusing on the scaling behavior of the magnetization. In particular, I will discuss non-central limit theorems for the magnetization, the emergence of conformal invariance at the critical point, and exponential decay of correlations in the near-critical regime.
Based on joint work with R. Conijn, C. Garban, J. Jiang, D. Kiss, and C.M. Newman.