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TMF, 1971, Volume 8, Number 3, Pages 401–412 (Mi tmf4420)  

This article is cited in 8 scientific papers (total in 8 papers)

Higher correlation functions of the Ising ferromagnet. The case of a linear model for spin $S=1/2$

M. P. Zhelifonov


Abstract: The Ising problem tor the spin $S\geqslant 1/2$ is solved by means of the two-time Green function method. It is shown that the chains of the coupled equations for Green functions are reduced to the closed systems of $L=2SP+1$ equations, $P$ being the coordination number of the lattice. The Green functions for $L=3,5,7,9,11$, found from these equations, make it possible to obtain sets of exact relationships for correlation functions. It is shown that these relationships lead to the complete solution of a dynamical problem in the case of a linear model $S=1/2$ (the two-particle and many-particle correlators are found) with various boundary conditions: the infinite chain of spins, the spin chain closed in a ring and the finite spin chain with fixed states of boundary spins.

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English version:
Theoretical and Mathematical Physics, 1971, 8:3, 920–927

Received: 08.06.1970
Revised: 18.02.1971

Citation: M. P. Zhelifonov, “Higher correlation functions of the Ising ferromagnet. The case of a linear model for spin $S=1/2$”, TMF, 8:3 (1971), 401–412; Theoret. and Math. Phys., 8:3 (1971), 920–927

Citation in format AMSBIB
\Bibitem{Zhe71}
\by M.~P.~Zhelifonov
\paper Higher correlation functions of the Ising ferromagnet. The case of a~linear model for spin $S=1/2$
\jour TMF
\yr 1971
\vol 8
\issue 3
\pages 401--412
\mathnet{http://mi.mathnet.ru/tmf4420}
\transl
\jour Theoret. and Math. Phys.
\yr 1971
\vol 8
\issue 3
\pages 920--927
\crossref{https://doi.org/10.1007/BF01029349}


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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. R. T. Galiullin, M. P. Zhelifonov, B. S. Nikitin, “Exact solution for the higher correlation functions of the linear spin-1 Ising model”, Theoret. and Math. Phys., 12:1 (1972), 720–722  mathnet  crossref
    2. V. A. Dobrovol'skii, A. R. Kessel, “Exact solution for linear quadrupole model of ising type”, Theoret. and Math. Phys., 16:1 (1973), 729–734  mathnet  crossref
    3. R. Z. Bariev, M. P. Zhelifonov, “Linear transformation matrix for the correlation functions of the Ising model”, Theoret. and Math. Phys., 25:2 (1975), 1132–137  mathnet  crossref  mathscinet
    4. R. R. Nigmatullin, V. A. Toboev, “Correlation functions for anisotropic heisenberg model in zero magnetic field”, Theoret. and Math. Phys., 68:1 (1986), 694–701  mathnet  crossref  mathscinet  isi
    5. R. R. Nigmatullin, V. A. Toboev, “Thermodynamics of the basic three-dimensional ferromagnetic models in the fluctuation approximation”, Theoret. and Math. Phys., 74:1 (1988), 79–88  mathnet  crossref  isi
    6. I. S. Donskaya, “Higher-order interactions in the linear ising model”, Theoret. and Math. Phys., 74:3 (1988), 324–328  mathnet  crossref  mathscinet  isi
    7. R. R. Nigmatullin, V. A. Toboev, “Thermodynamics of the two-dimensional and three-dimensional Ising models in the static fluctuation approximation”, Theoret. and Math. Phys., 80:1 (1989), 736–745  mathnet  crossref  mathscinet  isi
    8. I. S. Donskaya, A. R. Kessel, S. S. Lapushkin, “Nonresonant acoustic absorption of Ising magnet”, Theoret. and Math. Phys., 98:1 (1994), 100–106  mathnet  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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