HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Complete list of metadata

Contributor : Dmitry Chelkak Connect in order to contact the contributor
Submitted on : Tuesday, May 19, 2020 - 6:08:40 PM
Last modification on : Thursday, March 17, 2022 - 10:08:19 AM

Links full text


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



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



Record views