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 J. Sib. Fed. Univ. Math. Phys., 2015, Volume 8, Issue 1, Pages 31–37 (Mi jsfu403)

Cluster perturbation theory for 2d Ising model

Ilya D. Ivantsova, Sergey G. Ovchinnikovb

a Institute of Engineering Physics and Radio Electronics, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia
b Kirensky Institute of Physics, Akademgorodok, 50/38, Krasnoyarsk, 660036, Russia

Abstract: This paper deals with 2d Ising model in the scope of cluster perturbation theory. Ising model is defined on a two-dimensional square lattice, the amount of nearest neighbors $z=4$. Lattice is divided into clusters of a given size and a complete set of energy eigenvalues and eigenvectors of the cluster is defined by the diagonalization method. On the basis of this, Hubbard operators are constructed and Green function is calculated, taking into account intercluster interactions according to perturbation theory, it allows us to obtain the dependence of the magnetization on the temperature in the Hubbard-I approximation. Obtained results are compared with the exact solution of the two-dimensional Ising model.

Keywords: cluster perturbation theory, Ising model, X-operators.

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UDC: 517.9
Accepted: 20.11.2014
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Citation: Ilya D. Ivantsov, Sergey G. Ovchinnikov, “Cluster perturbation theory for 2d Ising model”, J. Sib. Fed. Univ. Math. Phys., 8:1 (2015), 31–37

Citation in format AMSBIB
\Bibitem{IvaOvc15} \by Ilya~D.~Ivantsov, Sergey~G.~Ovchinnikov \paper Cluster perturbation theory for 2d Ising model \jour J. Sib. Fed. Univ. Math. Phys. \yr 2015 \vol 8 \issue 1 \pages 31--37 \mathnet{http://mi.mathnet.ru/jsfu403}