Optimized machine learning methods for studying the thermodynamic behavior of complex spin systems

Kapitan D.Y., Ovchinnikov P.A., Soldatov K.S., Andriushchenko P.D., Kapitan V.U.
 pdf (9640K)

This paper presents a systematic study of the application of convolutional neural networks (CNNs) as an efficient tool for the analysis of critical and low-temperature phase states in two dimensional spin system models. The problem of calculating the dependence of the average energy $\langle E\rangle_T^{}$ on the spatial distribution of exchange integrals $J_k^{}$ for the Edwards – Anderson model on a square lattice with frustrated interactions is considered.

We further construct a single convolutional classifier of phase states of the ferromagnetic Ising model on square, triangular, honeycomb, and kagome lattices, trained on configurations generated by the Swendsen – Wang cluster algorithm. Сomputed temperature profiles of the averaged posterior probability of the high-temperature phase, form clear S-shaped curves that intersect in the vicinity of the theoretical critical temperatures and allow one to determine $T_c^{}$ for the kagome lattice without additional retraining.

It is shown that convolutional models substantially reduce the root-mean-square error (RMSE) compared with fully connected architectures and efficiently capture complex correlations between thermodynamic characteristics and the structure of magnetic correlated systems.

Keywords: Ising model, spin glass, machine learning, convolutional neural networks
Citation in English: Kapitan D.Y., Ovchinnikov P.A., Soldatov K.S., Andriushchenko P.D., Kapitan V.U. Optimized machine learning methods for studying the thermodynamic behavior of complex spin systems // Computer Research and Modeling, 2026, vol. 18, no. 1, pp. 25-40
Citation in English: Kapitan D.Y., Ovchinnikov P.A., Soldatov K.S., Andriushchenko P.D., Kapitan V.U. Optimized machine learning methods for studying the thermodynamic behavior of complex spin systems // Computer Research and Modeling, 2026, vol. 18, no. 1, pp. 25-40
DOI: 10.20537/2076-7633-2026-18-1-25-40
URL: http://crm-en.ics.org.ru/journal/article/3686/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2026 Kapitan D.Y., Ovchinnikov P.A., Soldatov K.S., Andriushchenko P.D., Kapitan V.U.

Indexed in Scopus

Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU

The journal is included in the Russian Science Citation Index

The journal is included in the RSCI

International Interdisciplinary Conference "Mathematics. Computing. Education"

Website Copyright © 2009–2026 Institute of Computer Science