We calculate the two-point correlation function and magnetic susceptibility in the anisotropic 2D Ising model on a lattice with one infinite and the other finite dimension, along which periodic boundary conditions are imposed. Using exact expressions for a part of lattice form factors, we propose the formulas for arbitrary spin matrix elements, thus providing a possibility to compute all multipoint correlation functions in the anisotropic Ising model on cylindrical and toroidal lattices. The scaling limit of the corresponding expressions is also analyzed.
The correlation function of two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor representation are obtained both for the ferromagnetic and paramagnetic regions of coupling constant. The peculiarities caused by the finite size of the system are discussed. The asymptotic behaviour of the corresponding quantities as functions of size is calculated. Some generalization of the obtained result is conjectured.