Spin matrix elements in 2D Ising model on the finite lattice

We present explicit formulas for all spin matrix elements in the 2D Ising model with the nearest neighbor interaction on the finite periodic square lattice. These expressions generalize the known results [Phys. Rev. D19, (1979), 2477--2479; hep-th/0107117; hep-th/0112167] (coincide with them in the appropriate limits) and fulfill the test of straightforward transfer matrix calculations for finite $N$.