# Magnetization in the zig-zag layered Ising model and orthogonal polynomials

Abstract : We discuss the magnetization $M_m$ in the $m$-th column of the zig-zag layered 2D Ising model on a half-plane using Kadanoff-Ceva fermions and orthogonal polynomials techniques. Our main result gives an explicit representation of $M_m$ via $m\times m$ Hankel determinants constructed from the spectral measure of a certain Jacobi matrix which encodes the interaction parameters between the columns. We also illustrate our approach by giving short proofs of the classical Kaufman-Onsager-Yang and McCoy-Wu theorems in the homogeneous setup and expressing $M_m$ as a Toeplitz+Hankel determinant for the homogeneous sub-critical model in presence of a boundary magnetic field.
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Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-02613070
Contributor : Dmitry Chelkak <>
Submitted on : Tuesday, May 19, 2020 - 6:08:40 PM
Last modification on : Monday, December 14, 2020 - 5:38:14 PM

### Identifiers

• HAL Id : hal-02613070, version 1
• ARXIV : 1904.09168

### Citation

Dmitry Chelkak, Clément Hongler, Rémy Mahfouf. Magnetization in the zig-zag layered Ising model and orthogonal polynomials. 2020. ⟨hal-02613070⟩

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