Title: Edge-coloured graph enumeration, the Ising model on random graphs, and Lee-Yang zeros
Abstract: Certain exponential integrals serve as generating functions of labelled edge-coloured graphs. Based on this, we derive asymptotics for the number of edge-coloured regular graphs with arbitrary weights assigned to different vertex structures. The asymptotic behaviour is governed by critical points of a polynomial. As an application, we give an exact solution of the Ising model on a random regular graph and show how its phase transition and critical exponents arise from our formula. Moreover, we establish connections to Lee–Yang phenomena in statistical physics by showing the accumulation of Ising partition function zeros along certain limit curves. These limit curves are semi-algebraic and reveal the location of phase transitions. Partially based on joint works with Michael Borinsky, Chiara Meroni and Shiyue Ren.
The advanced seminar begins at 4:00 pm s.t..