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 TMF, 1979, Volume 40, Number 1, Pages 95–99 (Mi tmf2807)

Correlation functions of the semi-infinite two-dimensional ising model

R. Z. Bariev

Abstract: The local magnetization of a spin at an arbitrary distance $(n-1)$ from the edge of the lattice is rigorously calculated for the semi-infinite two-dimensional Ising model. It is shown that as $T\to T_c$, $n\to\infty$ the magnetization takes the scaling form $\langle s_n\rangle =\tau^{1/8}F(x)$ ($\tau=|1-T/T_c|$, $x\sim 2n \tau$). Exact expressions are found for the function $F(x)$ and its asymptotic behavior at large and small $x$ is found.

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English version:
Theoretical and Mathematical Physics, 1979, 40:1, 623–626

Bibliographic databases:

Citation: R. Z. Bariev, “Correlation functions of the semi-infinite two-dimensional ising model”, TMF, 40:1 (1979), 95–99; Theoret. and Math. Phys., 40:1 (1979), 623–626

Citation in format AMSBIB
\Bibitem{Bar79} \by R.~Z.~Bariev \paper Correlation functions of the semi-infinite two-dimensional ising model \jour TMF \yr 1979 \vol 40 \issue 1 \pages 95--99 \mathnet{http://mi.mathnet.ru/tmf2807} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=543982} \transl \jour Theoret. and Math. Phys. \yr 1979 \vol 40 \issue 1 \pages 623--626 \crossref{https://doi.org/10.1007/BF01019245} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JG40800009} 

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This publication is cited in the following articles:
1. R. Z. Bariev, “Correlation functions of the semi-infinite two-dimensional ising model. II. Two-point correlation functions”, Theoret. and Math. Phys., 42:2 (1980), 173–178
2. E. I. Kornilov, V. B. Priezzhev, “Solution of the Kasteleyn model on a half-plane”, Theoret. and Math. Phys., 75:1 (1988), 408–416
3. R. Z. Bariev, “Correlation functions of semi-infinite two-dimensional Ising model. III. Influence of a “fixed” boundary”, Theoret. and Math. Phys., 77:1 (1988), 1090–1095
4. Schuricht, D, “Dynamical response functions in the quantum Ising chain with a boundary”, Journal of Statistical Mechanics-Theory and Experiment, 2007, P11004
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