Magnetic susceptibility of the 2D Ising model on the finite lattice

The generalization of the form factor representation of the 2D Ising model correlation function to the case of the general disposition of correlating spins on a cylinder is given. The magnetic susceptibility on the lattice where one of the dimensions $N$ is finite is calculated in both the para- and ferromagnetic regions of the Ising coupling parameter. The singularity structure in the complex temperature plane and the thermodynamic limit $N\to\infty$ are discussed