Lisovyy O. Correlations in finite lattice spin systems

Several approaches to the calculation of correlation functions and form factors in integrable two-dimensional models of statistical physics and quantum field theory have been developed. Exact expressions for pair correlation function in the anisotropic Ising model on a cylindrical lattice are found. Magnetic susceptibility and arbitrary spin matrix elements of the Ising model on the cylinder are calculated. A representation of the two-point correlators of the Ising field theory via the determinants of some infinite-dimensional matrices is obtained and a closed system of nonlinear differential equations for the correlators is derived. A theory of monodromy preserving deformations for Dirac equation on the cylinder with n marked points is constructed. We also define and calculate the tau function of the singular Dirac operator on the cylinder.