An accelerated exhaustive enumeration algorithm in the Ising model

An accelerated algorithm for the precise calculation of the lattice Ising model is presented. The algorithm makes it possible to calculate two-dimensional 8$\times$8 lattices for periodic boundary conditions on ordinary personal computers. In turn, the exact solution obtained by the proposed method makes it possible to check the effectiveness of various probabilistic approaches, in particular the Monte Carlo methods. The algorithm is applicable to various types of lattices.