Exact expressions of correlation functions between two spins in the boundary row of the two-dimensional rectangular Ising model with periodic-free boundary conditions and finite size

Abstract

We present exact expressions of correlation functions between two spins in the boundary row of the two-dimensional rectangular Ising model with periodic-free boundary conditions and finite size. Some properties of exact expressions obtained are discussed. The fundamental property of the Ising model that the long range order emerge as the temperature decrease is shown clearly; expressions of the correlation functions in the thermodynamic limit varies depending on the order of taking limits of two parameters L and N; the impact of different sizes on correlation functions is illustrated with the aid of diagrams. Expressions of the correlation function discussed in this paper in the thermodynamic limit has been presented by previous researchers, and we prove that expressions obtained in this article is identical in form to expressions provided by previous researchers in the thermodynamic limit.