Abstract:
Long-range Ising models exhibit phase coexistence and correlation decay mechanisms that differ substantially from those of finite-range systems, and are far less understood. In this talk I will present recent results on ferromagnetic Ising models with interaction $J_xy \sim |x-y|^{-\alpha}$, with emphasis on the decay of truncated correlations in the low-temperature regime. The key input is a notion of multiscaled contours, introduced to properly handle long-range systems, together with a cluster expansion adapted to this contour structure. I will describe how these tools lead to algebraic decay of the two-point function, with the exponent determined by the interaction itself, and discuss other problems where contour methods may be useful.
Biography:
Lucas Affonso is a postdoctoral researcher at the Institute of Mathematics and Statistics of the University of São Paulo (IME-USP), Brazil, and is currently a visiting postdoctoral fellow at New York University - Shanghai under the supervision of Prof. Roberto Fernández. His research interests lie in classical and quantum statistical mechanics, with a particular focus on systems with long-range interactions.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.