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 TMF, 1975, Volume 25, Number 2, Pages 280–288 (Mi tmf4073)

Linear transformation matrix for the correlation functions of the Ising model

R. Z. Bariev, M. P. Zhelifonov

Abstract: New formulation of the Ising problem is given, according to which the solution of the problem is reduced to diagonalizing the matrix of a certain linear transformation $W$ in the space of vectors composed of the correlation functions of the model. The structure of the new operator differs in a principal way from that of the usual transfer matrix. The matrix $W$ has a higher order and, for example, in the case of planar lattices it splits into separate blocks which can be easily diagonalized and lead to the exact solution of the problem.

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English version:
Theoretical and Mathematical Physics, 1975, 25:2, 1132–137

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Citation: R. Z. Bariev, M. P. Zhelifonov, “Linear transformation matrix for the correlation functions of the Ising model”, TMF, 25:2 (1975), 280–288; Theoret. and Math. Phys., 25:2 (1975), 1132–137

Citation in format AMSBIB
\Bibitem{BarZhe75} \by R.~Z.~Bariev, M.~P.~Zhelifonov \paper Linear transformation matrix for the correlation functions of the Ising model \jour TMF \yr 1975 \vol 25 \issue 2 \pages 280--288 \mathnet{http://mi.mathnet.ru/tmf4073} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=489627} \transl \jour Theoret. and Math. Phys. \yr 1975 \vol 25 \issue 2 \pages 1132--137 \crossref{https://doi.org/10.1007/BF01028959} 

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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”, Theoret. and Math. Phys., 40:1 (1979), 623–626
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