Lee-Yang phenomena in edge-coloured graph counting
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914234844053504 |
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| author | Wiesmann, Maximilian |
| author_facet | Wiesmann, Maximilian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02525 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lee-Yang phenomena in edge-coloured graph counting Wiesmann, Maximilian Combinatorics Statistical Mechanics Mathematical Physics Algebraic Geometry 05C31 (Primary) 05C30, 30C15, 32S20, 41A60, 82B20, 82B26 (Secondary) 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. |
| title | Lee-Yang phenomena in edge-coloured graph counting |
| topic | Combinatorics Statistical Mechanics Mathematical Physics Algebraic Geometry 05C31 (Primary) 05C30, 30C15, 32S20, 41A60, 82B20, 82B26 (Secondary) |
| url | https://arxiv.org/abs/2601.02525 |