- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Application of the path optimization method to a discrete spin system

Kouji Kashiwa1,*, Yusuke Namekawa2, Akira Ohnishi3,†, and Hayato Takase

  • 1Department of Computer Science and Engineering, Faculty of Information Engineering, Fukuoka Institute of Technology, Fukuoka 811-0295, Japan
  • 2Education and Research Center for Artificial Intelligence and Data Innovation, Hiroshima University, Hiroshima 730-0053, Japan
  • 3Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

  • *kashiwa@fit.ac.jp
  • †Deceased May 16, 2023.
PDF

Phys. Rev. D 108, 094504 – Published 13 November, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.094504

Abstract

The path optimization method, which is proposed to control the sign problem in quantum field theories with continuous degrees of freedom by machine learning, is applied to a spin model with discrete degrees of freedom. The path optimization method is applied by replacing the spins with dynamical variables, via the Hubbard-Stratonovich transformation, and the sum with the integral. The one-dimensional (Lenz-)Ising model with a complex coupling constant is used as a laboratory for the sign problem in the spin model. The average phase factor is enhanced by the path optimization method, indicating that the method can weaken the sign problem. Our result reproduces the analytic values with controlled statistical errors.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (46)

  1. P. de Forcrand, Proc. Sci. LAT2009 (2009) 010
  2. K. Nagata, Soryusironkenkyu 31, 1 (2020) (in Japanese); Prog. Part. Nucl. Phys. 127, 103991 (2022).
  3. E. Loh, Jr., J. Gubernatis, R. Scalettar, S. White, D. Scalapino, and R. Sugar, Phys. Rev. 41B, 9301 (1990).
  4. Y. Mori, K. Kashiwa, and A. Ohnishi, Prog. Theor. Exp. Phys. 2018, 023B04 (2018).
  5. A. Alexandru, P. F. Bedaque, H. Lamm, and S. Lawrence, Phys. Rev. D 97, 094510 (2018).
  6. F. Bursa and M. Kroyter, J. High Energy Phys. 12 (2018) 054.
  7. E. Witten, AMS/IP Stud. Adv. Math. 50, 347 (2011).
  8. Y. Mori, K. Kashiwa, and A. Ohnishi, Phys. Rev. D 96, 111501 (2017).
  9. K. Kashiwa, Y. Mori, and A. Ohnishi, Phys. Rev. D 99, 014033 (2019).
  10. K. Kashiwa, Y. Mori, and A. Ohnishi, Phys. Rev. D 99, 114005 (2019).
  11. A. Alexandru, P. F. Bedaque, H. Lamm, S. Lawrence, and N. C. Warrington, Phys. Rev. Lett. 121, 191602 (2018).
  12. Y. Mori, K. Kashiwa, and A. Ohnishi, Prog. Theor. Exp. Phys. 2019, 113B01 (2019).
  13. K. Kashiwa and Y. Mori, Phys. Rev. D 102, 054519 (2020).
  14. Y. Namekawa, K. Kashiwa, A. Ohnishi, and H. Takase, Phys. Rev. D 105, 034502 (2022).
  15. Y. Namekawa, K. Kashiwa, H. Matsuda, A. Ohnishi, and H. Takase, Phys. Rev. D 107, 034509 (2023).
  16. M. Giordano, K. Kapas, S. D. Katz, A. Pasztor, and Z. Tulipant, Phys. Rev. D 106, 054512 (2022).
  17. W. Detmold, G. Kanwar, M. L. Wagman, and N. C. Warrington, Phys. Rev. D 102, 014514 (2020).
  18. W. Detmold, G. Kanwar, H. Lamm, M. L. Wagman, and N. C. Warrington, Phys. Rev. D 103, 094517 (2021).
  19. A. Alexandru, G. Basar, P. F. Bedaque, and N. C. Warri ngton, Rev. Mod. Phys. 94, 015006 (2022).
  20. C. E. Berger, L. Rammelmüller, A. C. Loheac, F. Ehmann, J. Braun, and J. E. Drut, Phys. Rep. 892, 1 (2021).
  21. Y. Zhang, Z. Ghahramani, A. J. Storkey, and C. Sutton, in Advances in Neural Information Processing Systems, edited by F. Pereira, C. Burges, L. Bottou, and K. Weinberger (Curran Associates, Inc., 2012), Vol. 25.
  22. J. Ostmeyer, E. Berkowitz, T. Luu, M. Petschlies, and F. Pittler, Comput. Phys. Commun. 265, 107978 (2021).
  23. M. Fukuma and N. Umeda, Prog. Theor. Exp. Phys. 2017, 073B01 (2017).
  24. M. Fukuma, N. Matsumoto, and N. Umeda, Phys. Rev. D 100, 114510 (2019).
  25. W. Lenz, Phys. Z. 21, 613 (1920).
  26. E. Ising, Z. Phys. 31, 253 (1925).
  27. T.-D. Lee and C.-N. Yang, Phys. Rev. 87, 410 (1952).
  28. M. Fisher, Statistical Physics, Weak Interactions, Field Theory (University of Colorado Press, Boulder, 1965).
  29. M. G. Alford, S. Chandrasekharan, J. Cox, and U. J. Wiese, Nucl. Phys. B602, 61 (2001).
  30. S. Kim, P. de Forcrand, S. Kratochvila, and T. Takaishi, Proc. Sci. LAT2005 (2006) 166 [arXiv:hep-lat/0510069].
  31. K. Kashiwa and H. Kouno, Phys. Rev. D 103, 014014 (2021).
  32. M. Rodekamp, E. Berkowitz, C. Gäntgen, S. Krieg, T. Luu, and J. Ostmeyer, Phys. Rev. B 106, 125139 (2022).
  33. M. Fukuma and N. Matsumoto, Prog. Theor. Exp. Phys. 2021, 023B08 (2021).
  34. M. Fukuma, N. Matsumoto, and Y. Namekawa, Prog. Theor. Exp. Phys. 2021, 123B02 (2021).
  35. R. H. Swendsen and J.-S. Wang, Phys. Rev. Lett. 57, 2607 (1986).
  36. C. J. Geyer, in Computing Science and Statistics: Proceedings of 23rd Symposium on the Interface Foundation, Fairfax Station, 1991 (Interface Foundation of North America, 1991), p. 156.
  37. K. Hukushima and K. Nemoto, J. Phys. Soc. Jpn. 65, 1604 (1996).
  38. Z. Li and S. Arora, arXiv:1910.07454.
  39. A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga et al., in Advances in Neural Information Processing Systems (2019), Vol. 32.
  40. L. Bottou, Online learning in neural networks (1998).
  41. I. Loshchilov and F. Hutter, arXiv:1711.05101.
  42. A. Tomiya and Y. Nagai, arXiv:2103.11965.
  43. J. Liu, Y. Qi, Z. Y. Meng, and L. Fu, Phys. Rev. B 95, 041101 (2017).
  44. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).
  45. C. Ratti, M. A. Thaler, and W. Weise, Phys. Rev. D 73, 014019 (2006).
  46. K. Fukushima and V. Skokov, Prog. Part. Nucl. Phys. 96, 154 (2017).

Outline

Information

Phys. Rev. D 108, 094504– Published 13 November, 2023
  • Received 19 September 2023
  • Accepted 13 October 2023
Crossmark - Check for updates button
Creative Commons Logo

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. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation