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Detection of Berezinskii–Kosterlitz–Thouless transitions for the two-dimensional q-state clock models with neural networks

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Abstract

Using the technique of supervised neural networks (NN), we study the phase transitions of two-dimensional (2D) 6- and 8-state clock models on the square lattice. The employed NN has only one input layer, one hidden layer of 2 neurons, and one output layer. In addition, the NN is trained without using any prior information about the considered models. Interestingly, despite its simple architecture, the built supervised NN not only detects both the two Berezinskii–Kosterlitz–Thouless (BKT) transitions but also determines the transition temperatures with reasonable high accuracy. It is remarkable that an NN, which has a very simple structure and is trained without considering any input from the studied models, can be employed to study topological phase transitions. The outcomes shown here as well as those previously demonstrated in the literature suggest the feasibility of constructing a universal NN that is applicable to investigate the phase transitions of many systems.

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Data Availibility Statement

This manuscript has associated data in a data repository. [Authors’ comment: Data are available from the corresponding author on reasonable request.]

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Acknowledgements

Partial support from National Science and Technology Council (NSTC) of Taiwan (MOST 110-2112-M-003-015 and MOST 111-2112-M-003–011) is acknowledged. A preprint version has been appeared in arXiv (arXiv:2303.00439).

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  1. Department of Physics, National Taiwan Normal University, 88, Sec.4, Ting-Chou Rd, Taipei, 116, Taiwan

    Yuan-Heng Tseng & Fu-Jiun Jiang

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F-JJ proposed and supervised the project, and wrote up the manuscript. Y-HT conducted the calculations and analyzed the data.

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Tseng, YH., Jiang, FJ. Detection of Berezinskii–Kosterlitz–Thouless transitions for the two-dimensional q-state clock models with neural networks. Eur. Phys. J. Plus 138, 1118 (2023). https://doi.org/10.1140/epjp/s13360-023-04741-4

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