Geodesic
Correlation functions of the semi-infinite two-dimensional ising model
Teoretičeskaâ i matematičeskaâ fizika, Tome 40 (1979) no. 1, pp. 95-99

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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. 
@article{TMF_1979_40_1_a8,
     author = {R. Z. Bariev},
     title = {Correlation functions of the semi-infinite two-dimensional ising model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {95--99},
     publisher = {mathdoc},
     volume = {40},
     number = {1},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_40_1_a8/}
}
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R. Z. Bariev. Correlation functions of the semi-infinite two-dimensional ising model. Teoretičeskaâ i matematičeskaâ fizika, Tome 40 (1979) no. 1, pp. 95-99. http://geodesic.mathdoc.fr/item/TMF_1979_40_1_a8/