Diagonal Ising susceptibility: elliptic integrals, modular forms and Calabi-Yau equations. (English) Zbl 1273.82008
The magnetic susceptibility of the Ising model is defined in terms of the two-point spin correlation function as
\[
k_BT\cdot\chi=\sum_{M=-\infty}^{\infty}\sum_{N=-\infty}^{\infty}\{<\sigma_{0,0}\sigma_{M,N}>-\mathcal{M}^2\},
\]
where \(\mathcal{M}\) is the spontaneous magnetization of the Ising model. The authors present the exact expressions of the partial susceptibilities \(\chi_d^{(3)}\) and \(\chi_d^{(4)}\) for the diagonal susceptibility of the Ising model in terms of modular forms and Calabi-Yau equations.
Reviewer: Nasir N. Ganikhodjaev (Kuantan)
MSC:
82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
34M55 | Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies |
47E05 | General theory of ordinary differential operators |