Description
We show that specific exponential bivariate integrals serve as
generating functions of labeled edge-bicolored graphs. Based on this, we
prove an asymptotic formula for the number of regular edge-bicolored
graphs with arbitrary weights assigned to different vertex structures.
The asymptotic behavior is governed by the critical points of a
polynomial. As an application, we discuss the Ising model on a random
4-regular graph and show how its phase transitions arise from our formula.
Joint work with Chiara Meroni and Maximilian Wiesmann
Reference: arXiv:2409.18607
