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Entropy 2018, 20(4), 277; https://doi.org/10.3390/e20040277

Exact Expressions of Spin-Spin Correlation Functions of the Two-Dimensional Rectangular Ising Model on a Finite Lattice

Department of Journal, Central China Normal University, Wuhan 430079, China
Received: 8 February 2018 / Revised: 29 March 2018 / Accepted: 10 April 2018 / Published: 12 April 2018
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Abstract

We employ the spinor analysis method to evaluate exact expressions of spin-spin correlation functions of the two-dimensional rectangular Ising model on a finite lattice, special process enables us to actually carry out the calculation process. We first present some exact expressions of correlation functions of the model with periodic-periodic boundary conditions on a finite lattice. The corresponding forms in the thermodynamic limit are presented, which show the short-range order. Then, we present the exact expression of the correlation function of the two farthest pair of spins in a column of the model with periodic-free boundary conditions on a finite lattice. Again, the corresponding form in the thermodynamic limit is discussed, from which the long-range order clearly emerges as the temperature decreases. View Full-Text
Keywords: two-dimensional Ising model; spin-spin correlation functions; exact solution; short-range order; long-range order two-dimensional Ising model; spin-spin correlation functions; exact solution; short-range order; long-range order
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Mei, T. Exact Expressions of Spin-Spin Correlation Functions of the Two-Dimensional Rectangular Ising Model on a Finite Lattice. Entropy 2018, 20, 277.

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