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 TMF, 1985, Volume 63, Number 3, Pages 465–472 (Mi tmf4849)

Critical behavior of the ferromagnetic ising chain with interaction $J_{ij}=|i-j|^{-2}$

G. V. Matvienko

Abstract: For the one-dimensional ferromagnetic Isiag model with interaction that decreases inversely as the square of the distance between the lattice sites, high-temperature expansions of the susceptibility and specific heat are calculated to the eighth and ninth orders, respectively, in the reciprocal temperature. Analysis of the expansion of the susceptibility indicates that at the critical point its logarithm diverges in accordance with a power law with exponent $\nu=0,55\pm 0,03$. This estimate is close to the value $\nu=0.5$ obtained earlier by the renormalization-group method and is the first numerical confirmation of the predictions of the renormalization-group approach for systems with long-range interaction.

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English version:
Theoretical and Mathematical Physics, 1985, 63:3, 635–640

Bibliographic databases:

Citation: G. V. Matvienko, “Critical behavior of the ferromagnetic ising chain with interaction $J_{ij}=|i-j|^{-2}$”, TMF, 63:3 (1985), 465–472; Theoret. and Math. Phys., 63:3 (1985), 635–640

Citation in format AMSBIB
\Bibitem{Mat85} \by G.~V.~Matvienko \paper Critical behavior of the ferromagnetic ising chain with interaction~$J_{ij}=|i-j|^{-2}$ \jour TMF \yr 1985 \vol 63 \issue 3 \pages 465--472 \mathnet{http://mi.mathnet.ru/tmf4849} \transl \jour Theoret. and Math. Phys. \yr 1985 \vol 63 \issue 3 \pages 635--640 \crossref{https://doi.org/10.1007/BF01017511} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1985AWZ6400014} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. G. V. Matvienko, “Critical behavior of a plane Ising antiferromagnet with two-dimensional dipole interaction”, Theoret. and Math. Phys., 69:2 (1986), 1156–1163
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