Spectral Curve of Periodic Fisher Graphs

2010/08/23 by Zhongyang Li, Li, Zhongyang
Computer Science · Mathematics · Physics and Astronomy · #Complex Variables (math.CV) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Theoretical and Computational Physics #Topological and Geometric Data Analysis #math.CV #math.PR

paper · pdf · doi:10.48550/arxiv.1008.3936

27 pages

openalex publication_date 2010/08/23 · arxiv created 2012/04/12 · arxiv updated 2012/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the spectral curves of dimer models on periodic Fisher graphs, obtained from a ferromagnetic Ising model on ℤ². The spectral curve is defined by the zero locus of the determinant of a modified weighted adjacency matrix. We prove that either they are disjoint from the unit torus (\mathbbT²=\(z,w):|z|=1,|w|=1\) or they intersect \mathbbT² at a single real point.

Citations

• An introduction to the dimer model
• Amoebas of algebraic varieties

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