An Exact Closed Formula of a Spin-spin Correlation Function of the Two-Dimensional Ising Model with Finite Size

摘要

Some expressions of spin-spin correlation functions of the two-dimensional Ising model in the thermodynamic limit have been obtained, however, so far, no one correlation function that can show long range order of the model with finite size has been obtained. The purpose of this paper is to fill this gap. We present an exact closed formula for the correlation functions of the farthest pairs of spins in a column of the two-dimensional rectangular Ising model with periodic-free boundary condition and finite size by the spinor analysis method. The concrete expression correct to order of magnitude of such correlation functions is presented, from which it is shown clearly how long range order emerges as the decrease of the temperature. Some properties are discussed.