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Exact relations for correlation functions in the general Ising model

M.P. Zhelifonov, R. T. Galiullin

Physics Letters AJan 1, 19736 citations

Off-axis correlation functions in the isotropicd=2 Ising model

Robert E. Shrock, Ranjan K. Ghosh

We present exact explicit expressions for the spin-spin correlation functions 〈${\ensuremath{\sigma}}_{0}$,0${\mathrm{\ensuremath{\sigma}}}_{\mathrm{m}}$,n〉 for (m,n)=(2,1), (3,1), (3,2), (4,1), (4,2), and (4,3) in the isotropic d=2 Ising model. We also infer a general structural formula for arbitrary 〈${\ensuremath{\sigma}}_{0}$,0${\mathrm{\ensuremath{\sigma}}}_{\mathrm{m}}$,n〉 in terms of complete elliptic integrals K and E.We present exact explicit expressions for the spin-spin correlation functions 〈${\ensuremath{\sigma}}_{0}$,0${\mathrm{\ensuremath{\sigma}}}_{\mathrm{m}}$,n〉 for (m,n)=(2,1), (3,1), (3,2), (4,1), (4,2), and (4,3) in the isotropic d=2 Ising model. We also infer a general structural formula for arbitrary 〈${\ensuremath{\sigma}}_{0}$,0${\mathrm{\ensuremath{\sigma}}}_{\mathrm{m}}$,n〉 in terms of complete elliptic integrals K and E.

Physical review. B, Condensed matterFeb 1, 198516 citations

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

Mei Tao

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.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.

arXiv:2608.19274Aug 18, 20260 citations

Computation of correlation functions of the two dimensional Ising model

Bülent Kutlu, Nevzat AKTEKİN

Physica A Statistical Mechanics and its ApplicationsMay 1, 199512 citations

Spin-Spin Correlation Functions for the Two-Dimensional Ising Model

Barry M. McCoy, Craig A. Tracy, Tai Tsun Wu

Springer eBooksJan 1, 19776 citations

Row Correlation Functions of the Two-Dimensional Ising Model

David A. Pink

Expressions for many-site correlation functions of a square-lattice Ising model have been derived for the case in which all sites lie in the same row. The results involve expressions for minors of Toeplitz matrices which are obtained by the Wiener-Hopf technique. We derive an expression for the magnetization at any site in a row if a finite number of defect bonds are distributed at given positions in that row; this expression can be used to study the effect of a dislocation. Some remarks about the decoupling of correlation functions are made.Expressions for many-site correlation functions of a square-lattice Ising model have been derived for the case in which all sites lie in the same row. The results involve expressions for minors of Toeplitz matrices which are obtained by the Wiener-Hopf technique. We derive an expression for the magnetization at any site in a row if a finite number of defect bonds are distributed at given positions in that row; this expression can be used to study the effect of a dislocation. Some remarks about the decoupling of correlation functions are made.

Physical ReviewDec 10, 19696 citations

Exact expressions for row correlation functions in the isotropicd=2 ising model

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Exact expressions for row correlation functions in the isotropicd=2 ising model

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