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Preprints, Working Papers, ... Year : 2020

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.

Dates and versions

hal-02613070 , version 1 (19-05-2020)

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