Loop models and the universal distribution of the loop lengths

by Prof. Daniel Ueltschi (The University of Warwick)

Thursday 4 May 2023, 14:00 → 15:30 Europe/Rome

Rectorate/Building-Auditorium (GSSI)

I will review several models that consist of one-dimensional loops living in the three-dimensional space.

These models describe bosonic systems, and classical or quantum spin systems.

Their common feature is that the joint distribution of their loop lengths has universal behaviour: it is always a Poisson-Dirichlet distribution.

Most of this theory is conjectural, but it is backed by numerical studies and some partial rigorous results.