Abstract:
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.
Biography:
Yucheng Liu received his Ph.D. from the University of British Columbia in 2025 and is currently a postdoctoral researcher at Peking University. His research focuses on probability and statistical mechanics, with particular interests in critical and near-critical phenomena of statistical mechanical models.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.