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arXiv · 2207.09268

On General-n Coefficients in Series Expansions for Row Spin-Spin Correlation Functions in the Two-Dimensional Ising Model

Robert Shrock
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Abstract

We consider spin-spin correlation functions for spins along a row, $R_n = \langle \sigma_{0,0}\sigma_{n,0}\rangle$, in the two-dimensional Ising model. We discuss a method for calculating general-$n$ expressions for coefficients in high-temperature and low-temperature series expansions of $R_n$ and apply it to obtain such expressions for several higher-order coefficients. In addition to their intrinsic interest, these results could be useful in the continuing quest for an ordinary differential equation whose solution would determine $R_n$, analogous to the known ordinary differential equation whose solution determines the diagonal correlation function $\langle \sigma_{0,0}\sigma_{n,n}\rangle$ in this model.

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Robert Shrock. 2022-07-19. On General-n Coefficients in Series Expansions for Row Spin-Spin Correlation Functions in the Two-Dimensional Ising Model. https://doi.org/10.1088/1751-8121%2Fac9654

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