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Neural network evidence of a weakly first-order phase transition for the two-dimensional 5-state Potts model

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Abstract

A universal (supervised) neural network (NN), which is trained only once on a one-dimensional lattice of 200 sites, is employed to study the phase transition of the two-dimensional (2D) 5-state ferromagnetic Potts model on the square lattice. In particular, the NN is obtained by using two artificially made configurations as the training set. Due to the unique features of the employed NN, results associated with systems consisting of over 4,000,000 spins can be obtained with ease, and convincing NN evidence showing that the investigated phase transition is weakly first order is reached.

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Data Availability 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 Ministry of Science and Technology of Taiwan is acknowledged (MOST 110-2112-M-003-015). Data will be made available upon reasonable request. A preprint version has been appeared in arXiv (arXiv:2111.14063).

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Authors and Affiliations

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

    Yuan-Heng Tseng, Yun-Hsuan Tseng & Fu-Jiun Jiang

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  1. Yuan-Heng Tseng
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  2. Yun-Hsuan Tseng
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  3. Fu-Jiun Jiang
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Contributions

FJJ proposed and supervised the project, and wrote up the manuscript. YHT and YHT conducted the calculations and analyzed the data.

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Correspondence to Fu-Jiun Jiang.

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Tseng, YH., Tseng, YH. & Jiang, FJ. Neural network evidence of a weakly first-order phase transition for the two-dimensional 5-state Potts model. Eur. Phys. J. Plus 137, 1374 (2022). https://doi.org/10.1140/epjp/s13360-022-03597-4

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