Federico Camia

Scaling behavior and decay of correlations in the critical and near-critical planar Ising model

The Ising model, introduced by Lenz in 1920 to describe ferromagnetism, is one of 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 that make the connection between the planar Ising model and the corresponding Euclidean field theory increasingly more explicit. In this talk, I will introduce the Ising model and discuss recent results on its critical and near-critical scaling limits. I will focus in particular on the scaling behavior of the magnetization field at criticality and on the 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.)