The torus plateau for the high-dimensional Ising model

ESB 4127

We report recent progress in the study of statistical mechanical models on the discrete torus (finite box in the lattice with periodic boundary conditions). In high dimensions, the torus two-point function near the infinite-volume critical point levels off at large distance to a constant called the "torus plateau." We focus on the Ising model in dimensions $d > 4$ but will also discuss the general theory. If time permits, we will discuss the percolation picture from the random current representation of the Ising model, through which we compare the Ising model on the torus with the model on the infinite lattice. This is based on joint works with Romain Panis, Jiwoon Park, and Gordon Slade.