Far Eastern Mathematical Journal

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An enumeration decomposition algorithm for solving the Ising mode

Trukhin V.O., Lobanova E.A., Anisich A.I., Makarova K.V., Makarov A.G., Nefedev K.V.

2025, issue 1, P. 102-112 DOI: https://doi.org/10.47910/FEMJ202509

Abstract

The article presents a novel algorithm for the complete enumeration of spin configurations in the Ising model on a square lattice. Particular attention is given to the parallel algorithmization of computations on central processing units (CPUs) using OpenMP and on graphics processing units (GPUs) using CUDA. The structure of the algorithm is described, including its main implementation steps, as well as its application to solving problems in statistical thermodynamics, specifically the calculation of the density of states. A performance comparison is conducted between the proposed algorithm and sequential enumeration algorithms implemented in Python and C. The results demonstrate that the proposed approach significantly accelerates computations and enables efficient analysis of square-lattice spin systems in the Ising model with sizes up to $10 \times 10$ nodes (100 spins) and with an arbitrary distributions of exchange constants.

Keywords: decomposition algorithm, Ising model, parallel computing.

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