Mirror symmetry of elliptic curves and Ising model

Details Mirror symmetry of elliptic curves and Ising model Mirror symmetry of elliptic curves and Ising model

1995-09-09

arxiv.org/abs/hep-th/9509051v1

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, Latex

Scientific paper

10.1016/0393-0440(95)00060-7

We study the differential equations governing mirror symmetry of elliptic curves, and obtain a characterization of the ODEs which give rise to the integral ${\bf q}$-expansion of mirror maps. Through theta function representation of the defining equation, we express the mirror correspondence in terms of theta constants. By investigating the elliptic curves in $X_9$-family, the identification of the Landau-Ginzburg potential with the spectral curve of Ising model is obtained. Through the Jacobi elliptic function parametrization of Boltzmann weights in the statistical model, an exact Jacobi form-like formula of mirror map is described .

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