2003/12/31 by Shu-Chiuan Chang, SHU-CHIUAN CHANG, Masuo Suzuki +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Algebraic number #Complex Systems and Time Series Analysis #Correlation #Correlation function (quantum field theory) #Ising model #Lattice (music) #Monotonic function #Random Matrices and Applications #Series (stratigraphy) #Spins #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1142/s0217979204023842
published in International Journal of Modern Physics B 18(02), 275-287 (World Scientific) · 13 pages, section 5 removed
openalex publication_date 2004/01/20 · arxiv created 2004/02/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study long-range correlation functions of the rectangular Ising lattice with cyclic boundary conditions. Specifically, we consider the situation in which two spins are on the same column, and at least one spin is on or near free boundaries. The low-temperature series expansions of the correlation functions are presented when the spin–spin couplings are the same in both directions. The exact correlation functions can be obtained by D log Padé for the cases with simple algebraic resultant expressions. The present results show that when the two spins are infinitely far from each other, the correlation function is equal to the product of the row magnetizations of the corresponding spins, as expected. In terms of low-temperature series expansions, the approach of this m th row correlation function to the bulk correlation function for increasing m can be understood from the observation that the dominant terms of their series expansions are the same successively in the above two correlation functions. The number of these dominant terms increases monotonically as m increases.