Spectral Curve of Periodic Fisher Graphs

Details Spectral Curve of Periodic Fisher Graphs Spectral Curve of Periodic Fisher Graphs

2010-08-23

arxiv.org/abs/1008.3936v5

Mathematics

Complex Variables

27 pages

Scientific paper

We study the spectral curves of dimer models on periodic Fisher graphs, obtained from a ferromagnetic Ising model on $\mathbb{Z}^2$. 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 ($\mathbb{T}^2=\{(z,w):|z|=1,|w|=1\}$) or they intersect $\mathbb{T}^2$ at a single real point.

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