Spectral Curve of Periodic Fisher Graphs

Abstract

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.

27 pages

References in corpus (1)

• An introduction to the dimer model

Cited by in corpus (1)

• The critical temperature for the Ising model on planar doubly periodic graphs