From Holonomy of the Ising Model Form Factors to n-Fold Integrals and the Theory of Elliptic Curves

From Holonomy of the Ising Model Form Factors to n-Fold Integrals and the Theory of Elliptic Curves

We recall the form factors $f^(j)_{N,N}$ corresponding to the $lambda$-extension $C(N,N; lambda)$ of the two-point diagonal correlation function of the Ising model on the square lattice and their associated linear differential equations which exhibit both a "Russian-doll" nesting, and a de...

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Bibliographic Details
Main Authors: Salah Boukraa, Saoud Hassani, Jean-Marie Maillard, Nadjah Zenine
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2007-10-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
form factors
sigma form of Painlevé VI
two-point correlation functions of the lattice Ising model
Fuchsian linear differential equations
complete elliptic integrals
elliptic representation of Painlevé VI
scaling limit of the Ising model
susceptibility of the Ising model
singular behaviour
apparent singularities
Landau singularities
pinch singularities
modular forms
Landen transformation
isogenies of elliptic curves
complex multiplication
Heegner numbers
moduli space of curves
pointed curves
Online Access:http://www.emis.de/journals/SIGMA/2007/099/

Internet

http://www.emis.de/journals/SIGMA/2007/099/

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