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

Friday, 19 April, 2019

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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×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.


Dmitry Chelkak
Clément Hongler
Rémy Mahfouf