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Cluster Method of Constructing Bethe Approximation for the Ising Model of a Dilute Magnet

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The paper offers an interpretation of Bethe approximation based on comparison of spin clusters of different sizes on the Cayley tree. Based on this interpretation, the authors suggested the method to construct Bethe approximation for the node- or bond-diluted Ising magnet. The method provides an accurate value of the percolation threshold for the Bethe lattice. For different variations of this method, the authors constructed spontaneous magnetizations at zero and final temperatures as a function of concentration of magnetic atoms and found an analytical expression for the critical indicator of the correlation length.

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References

  1. J. M. Ziman, Models of Disorder: The Theoretical Physics of Homogeneously Disordered Systems, Cambridge University Press (1979).

  2. Yu. A. Izyumov, M. V. Medvedev, Theory of Magnetic-Ordered Crystals with Impurities [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  3. R. Folk, Yu. Golovach, T. Yavorskii, Physics-Uspekhi [in Russian], 173, 175–192 (2003).

  4. V. S. Dotsenko, Physics-Uspekhi, 38, Issue 5, 457–496 (1995).

  5. B. N. Shalaev, Physics of Solid State, 52, Issue 1, 87–90 (2010).

  6. B. N. Shalaev, JETP, 46, Issue 6, 1204–1207 (1977).

  7. R. J. Birgeneau et al., Phys. Rev. B., 27, 6747 (1983).

    Article  ADS  Google Scholar 

  8. R. J. Baxter, Exactly Solved Models in Statistical Mechanics, Academic Press (1982).

  9. L. A. Serkov, Theor. Math. Phys., 92, Issue 1, 759–762 (1992).

  10. J. O. Indekeu, A. Maritan, and A. L. Stella, J. Phys. A., 15, 291 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  11. S. V. Semkin, V. P. Smagin, Physics of Solid State, 56, Issue 6, 1105–1109 (2014).

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Authors and Affiliations

  1. Vladivostok State University of Economics and Service, Vladivostok, Russia

    S. V. Semkin & V. P. Smagin

Authors
  1. S. V. Semkin
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  2. V. P. Smagin
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Correspondence to S. V. Semkin.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 140–145, October, 2017.

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Semkin, S.V., Smagin, V.P. Cluster Method of Constructing Bethe Approximation for the Ising Model of a Dilute Magnet. Russ Phys J 60, 1803–1810 (2018). https://doi.org/10.1007/s11182-018-1285-x

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  • DOI: https://doi.org/10.1007/s11182-018-1285-x

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