Mathematics & Physics 2015, 8(1), 31–37 УДК 517.9 Cluster Perturbation Theory for 2d Ising Model Ilya D. Ivantsov∗ Institute of Engineering Physics and Radio Electronics Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Sergey G.Ovchinnikov† Kirensky Institute of Physics Akademgorodok, 50/38, Krasnoyarsk, 660036 Russia Received 10.09.2014, received in revised form 12.10.2014, accepted 20.11.2014 This paper deals with 2d Ising model in the scope of cluster perturbation theory. <...> 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. <...> The presence of and exact solution in one- and two- dimensional cases is one of the main advantages of this model, it allows us to check numerical methods of solving statistical physics problems using it. <...> Expression for spontaneous magnetization was obtained by Onsager in 1949 and the full derivation was represented by Yang in 1952 [2]. <...> In the isotropic case the spontaneous magnetization has the following form M = 1−sinh−4 J kT temperature Tc = J k ln(1+√2) ≈ 1.135J k . 1/8 , where k is for Boltzmann constant. <...> The value of the critical exponent β = 1/8, and the critical 1 In the case of mean-field theory (In this case it is corresponding to Hubbard-I decoupling) results correspond to exact solution badly. <...> The amount of critical exponent β and critical temperature are, respectively β = 1/2 and Tc = 2. ∗ilyaivancov@mail.ru †sgo@iph.krasn.ru Siberian Federal University. <...> All rights reserved c – 31 – Ilya D. Ivantsov, Sergey G.Ovchinnikov Cluster Perturbation Theory for 2d Ising Model Over last two decades much attention is paid to the cluster approach during lattice models study [3]. <...> In this paper Cluster Perturbation Theory (CPT), previously used in the solution of Hubbard model [4]. <...> In this approach <...>