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

Form factor representation of the correlation function of the 2D Ising model on a cylinder is generalized to the case of arbitrary disposition of correlating spins. The magnetic susceptibility on a lattice, one of whose dimensions ($N$) is finite, is calculated in both para- and ferromagnetic regions of parameters of the model. The singularity structure of the susceptibility in the complex temperature plane at finite values of $N$ and the thermodynamic limit $N\to\infty$ are discussed.