Lee-Yang phenomena in edge-coloured graph counting
Combinatorics
2026-01-07 v1 Statistical Mechanics
Mathematical Physics
Algebraic Geometry
math.MP
Abstract
We study the accumulation of zeros of a polynomial arising from the enumeration of edge-coloured graphs along certain limit curves. The polynomial is a variant of an edge-chromatic polynomial, which specialises to the partition function of the ferromagnetic Ising model on a random regular graph. We call this accumulation behaviour a Lee-Yang phenomenon in analogy with the Lee-Yang theorem. The limiting loci are semialgebraic and arise from anti-Stokes curves of an exponential integral.
Keywords
Cite
@article{arxiv.2601.02525,
title = {Lee-Yang phenomena in edge-coloured graph counting},
author = {Maximilian Wiesmann},
journal= {arXiv preprint arXiv:2601.02525},
year = {2026}
}
Comments
19 pages, 3 figures. Comments are welcome!