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  • Open Access

Detecting the three-dimensional Ising model phase transition with a ground-state-trained autoencoder

Ahmed Abuali1,*, David A. Clarke2,†, Morten Hjorth-Jensen3,‡, Ioannis Konstantinidis4, Claudia Ratti1, and Jianyi Yang4

  • *Contact author: amabuali@uh.edu; ahmed.abuali1975@gmail.com
  • †Contact author: clarke.davida@gmail.com
  • ‡Contact author: mhjensen@uio.no
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APS Open Sci. 1, 000072 – Published 27 July, 2026

DOI: https://doi.org/10.1103/h8n4-94g4

Abstract

We develop a one-class, deep-learning framework to detect the phase transition and recover critical behavior of the three-dimensional (3D) Ising model. A 3D convolutional autoencoder (CAE) is trained on ground-state configurations only, without prior knowledge of the critical temperature, the Hamiltonian, or the order parameter. After training, the model is applied to Monte Carlo configurations across a wide temperature range and different lattice sizes. The mean-square reconstruction error is shown to be sensitive to the transition. Finite-size scaling of the peak location for the reconstruction error susceptibility yields the critical temperature Tc=4.5128(58), in excellent agreement with the known value. Additionally, we obtain an estimate of the correlation-length critical exponent, ν=0.63(27), also consistent with results from the literature. Our results show that a one-class CAE, trained on zero-temperature configurations only, can recover nontrivial critical behavior of the 3D Ising model.

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APS Open Sci. 1, 000072– Published 27 July, 2026
Vol. 1
  • Received 31 March 2026
  • Revised 8 July 2026
  • Accepted 16 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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