Simple solution of two-dimensional ising model on a torus in terms of Grassmann integrals

A simple method is proposed for exact solution of the two-dimensional Ising model on a torus (lattice of finite size with periodic boundary conditions). The problem is solved through construction of a Grassmann representation for the partition function. The mirror Grassmann factorization for the Boltzmann weights and a special identity for Grassmaan functions are used. The method is mathematically completely rigorous.