University of Sydney Algebra Seminar

Nikolai Iorgov (Bogolyubov Institute for Theoretical Physics)

Friday 21 October, 12:05-12:55pm, Carslaw 175

Ising correlations and elliptic determinants

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 eigenvectors 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 O. Lisovyy. (The talk is based on arXiv:1012.2856).