Speaker: Maximilian Wiesmann

Abstract: Certain exponential integrals serve as generating functions of labeled edge-colored graphs. Based on this, we derive asymptotics for the number of edge-colored graphs with arbitrary weights assigned to different vertex structures. The asymptotic behavior is governed by critical points of a polynomial. As an application, we discuss the Ising model on a random graph and show how its phase transitions arise from our formula. Moreover, we establish connections to Lee–Yang phenomena in statistical physics by showing the accumulation of Lee-Yang zeros along certain limit curves. These limit curves reveal the location of phase transitions. Based on joint work with Michael Borinsky and Chiara Meroni.