https://doi.org/10.1140/epjp/s13360-023-04741-4
Regular Article
Detection of Berezinskii–Kosterlitz–Thouless transitions for the two-dimensional q-state clock models with neural networks
Department of Physics, National Taiwan Normal University, 88, Sec.4, Ting-Chou Rd, 116, Taipei, Taiwan
Received:
30
October
2023
Accepted:
24
November
2023
Published online:
16
December
2023
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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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
