Ising Correlations and Elliptic Determinants |
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Authors: | N Iorgov O Lisovyy |
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Institution: | 1.Bogolyubov Institute for Theoretical Physics,Kyiv,Ukraine;2.Max-Planck-Institut für Mathematik,Bonn,Germany;3.Laboratoire de Mathématiques et Physique Théorique CNRS/UMR 6083,Université de Tours, Parc de Grandmont,Tours,France |
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Abstract: | Correlation functions of the two-dimensional Ising model on the periodic lattice can be expressed in terms of form factors—matrix
elements of the spin operator in the basis of common eigenstates of the transfer matrix and translation operator. Free-fermion
structure of the model implies that any multiparticle form factor is given by the pfaffian of a matrix constructed from the
two-particle ones. Crossed two-particle form factors can be obtained by inverting a block of the matrix of linear transformation
induced on fermions by the spin conjugation. We show that the corresponding matrix is of elliptic Cauchy type and use this
observation to solve the inversion problem explicitly. Non-crossed two-particle form factors are then obtained using theta
functional interpolation formulas. This gives a new simple proof of the factorized formulas for periodic Ising form factors,
conjectured by A. Bugrij and one of the authors. |
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