Correlation function of the two-dimensional Ising model on a finite lattice: I

The spin spin correlation function of the two-dimensional Ising model with nearest-neighbor interaction is calculated on a finite lattice with periodic boundary conditions. The representations, which are analogous to the form-factor representation, are obtained for the ferromagnetic and paramagnetic domains of the interaction parameter. We discuss the effects of the finiteness of the system. We investigate the asymptotic dependence of the corresponding quantities on the lattice size.